Algebra Calculator

Interactive calculator

Algebra calculator

Type a supported algebra problem directly, get the answer with visible steps, or open a focused tool for systems, slope, quadratics, and matrices.

Ready · Direct solver + 5 toolsInteractive tool

WorkspaceCalculator controls

Use the controls below to enter, calculate, and review.

Direct algebra solver

Type the problem exactly as you see it

Enter an equation, polynomial expression, or finite product. The solver identifies the supported problem type and shows the reasoning—not only the final answer.

Answerx = -1

Linear equation

Interpreted problem

5x - 6 = 3x - 8

Shown in full

Solution steps

Simplify both sides5x − 6 = 3x − 8
Expand products and powers on each side, then combine like terms.
Write standard form2x + 2 = 0
Subtract the right side from both sides so every term is on the left.
Isolate the variable term2x = -2
Add -2 to both sides after collecting the x terms.
Divide by the coefficientx = -1
Divide both sides by 2.

This reviewed solver covers bounded one-variable polynomial algebra and finite products. It reports unsupported notation instead of guessing.

More algebra tools5 focused calculators

Choose a structured calculator for linear systems, coefficient-based equations, coordinate slope, quadratic roots, or matrix multiplication.

Choose an algebra calculator

Solve an equation: Solve ax+b=cx+d from four real coefficients. Only the declared fields below are evaluated; this is not an arbitrary expression parser.

Guided calculator

Solve equation setup

Enter the known values, calculate once, and review the main answer with its supporting details.

Formula 1.0.04 inputs

How to use: Enter the requested values below, then select Calculate to review your result.

Solves the declared real linear form ax+b=cx+d and distinguishes one, no, or infinitely many solutions.

Inputs

Enter your values

Required fields stay visible; optional choices appear when needed.

Step 1

One-box algebra studio

Translate a written algebra problem before asking for an answer

A useful algebra calculator is a reading partner as much as an arithmetic engine: it should preserve the structure you typed, name the operation it recognized, and make every rewrite traceable.

Step-by-step guide · One-box algebra studio

A garden-border expression shows why equivalent is not identical-looking

Direct equation scope: linear or quadratic in x
Expression scope: bounded one-variable polynomials
Reasoning trail: normalized input plus ordered steps

Distribute by place, not by memory
Multiply each term in the first factor by each term in the second: x·x, x·(−1), 3·x, and 3·(−1). This gives x²−x+3x−3. The four products account for the four subrectangles in an area model.
Combine only matching powers
The terms −x and 3x are like terms, so their coefficients add to 2. Neither can merge with x² or −3. The standard form is x²+2x−3, equivalent to the original product for every supported x.
Check at a harmless value
At x=4, the factored expression is 7·3=21 and the expanded form is 16+8−3=21. A numerical spot check does not prove an identity, but it often exposes a missing product or sign error before the result is reused.

Translate a written algebra problem before asking for an answer: Suppose a rectangular planting bed has length x+3 meters and width x−1 meters. The expression (x+3)(x−1) describes its area without choosing a particular x.

Algebra begins by deciding what each symbol is doing

The same marks can play different roles. In 4x+7, x is a variable, 4 is its coefficient, and 7 is a constant. In x²−5x+6=0, the equals sign turns an expression into an equation whose solutions must make both sides equal. In (x+2)(x−2), adjacency means multiplication. Naming those roles prevents the common mistake of combining unlike terms or treating an expression as though it asked for a value of x.

The direct workbench recognizes a bounded set of classroom forms: polynomial simplification, real factorization through quadratics, equations through degree two, and finite products with explicit integer bounds. If the assignment already provides four coefficients for ax+b=cx+d, the narrower solve equation calculator offers a more constrained path. Choosing the narrowest suitable tool makes the assumptions easier to audit.

A garden-border expression shows why equivalent is not identical-looking

Suppose a rectangular planting bed has length x+3 meters and width x−1 meters. The expression (x+3)(x−1) describes its area without choosing a particular x.

Distribute by place, not by memory
Multiply each term in the first factor by each term in the second: x·x, x·(−1), 3·x, and 3·(−1). This gives x²−x+3x−3. The four products account for the four subrectangles in an area model.
Combine only matching powers
The terms −x and 3x are like terms, so their coefficients add to 2. Neither can merge with x² or −3. The standard form is x²+2x−3, equivalent to the original product for every supported x.
Check at a harmless value
At x=4, the factored expression is 7·3=21 and the expanded form is 16+8−3=21. A numerical spot check does not prove an identity, but it often exposes a missing product or sign error before the result is reused.

Solving and simplifying answer different questions

Simplification preserves the value

A simplified expression is another representation of the same function. No particular x is selected. Use the simplify calculator when expanding products and collecting powers is the whole task.

Solving selects admissible inputs

An equation asks which x-values make a statement true. A quadratic can have two, one repeated, or two complex roots; the quadratic formula calculator exposes that classification from a, b, and c.

Factoring exposes multiplication structure

Writing x²−5x+6 as (x−2)(x−3) reveals zeros 2 and 3, but factoring over the reals is not available for every polynomial. A negative discriminant signals that a quadratic has no real linear factorization.

An algebra answer should survive four quick audits

Read the normalized problem and confirm that implicit multiplication, minus signs, parentheses, and powers were interpreted as intended.
Trace every equality as an equivalence, not merely as an instruction to move a term across the page; the underlying justification is an equality property or distribution.
Substitute each proposed solution into the original equation, especially after squaring, clearing denominators, or using a numerical approximation outside this bounded workbench.
Use the system of equations calculator when two or three variables must satisfy several equations simultaneously; a one-variable parser cannot infer that larger model.

Important limitations

Direct entry is intentionally bounded to one real variable x, polynomial degree 20 or below for simplification, equations through degree two, real linear factors, and finite products with constant integer bounds. It is not an unrestricted CAS, proof engine, inequality solver, camera solver, or arbitrary LaTeX interpreter.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

One-box algebra studio

Translate a written algebra problem before asking for an answer

A useful algebra calculator is a reading partner as much as an arithmetic engine: it should preserve the structure you typed, name the operation it recognized, and make every rewrite traceable.

Step-by-step guide · One-box algebra studio

A garden-border expression shows why equivalent is not identical-looking

Direct equation scope: linear or quadratic in x
Expression scope: bounded one-variable polynomials
Reasoning trail: normalized input plus ordered steps

Distribute by place, not by memory
Multiply each term in the first factor by each term in the second: x·x, x·(−1), 3·x, and 3·(−1). This gives x²−x+3x−3. The four products account for the four subrectangles in an area model.
Combine only matching powers
The terms −x and 3x are like terms, so their coefficients add to 2. Neither can merge with x² or −3. The standard form is x²+2x−3, equivalent to the original product for every supported x.
Check at a harmless value
At x=4, the factored expression is 7·3=21 and the expanded form is 16+8−3=21. A numerical spot check does not prove an identity, but it often exposes a missing product or sign error before the result is reused.

Algebra begins by deciding what each symbol is doing

A garden-border expression shows why equivalent is not identical-looking

Suppose a rectangular planting bed has length x+3 meters and width x−1 meters. The expression (x+3)(x−1) describes its area without choosing a particular x.

Distribute by place, not by memory
Multiply each term in the first factor by each term in the second: x·x, x·(−1), 3·x, and 3·(−1). This gives x²−x+3x−3. The four products account for the four subrectangles in an area model.
Combine only matching powers
The terms −x and 3x are like terms, so their coefficients add to 2. Neither can merge with x² or −3. The standard form is x²+2x−3, equivalent to the original product for every supported x.
Check at a harmless value
At x=4, the factored expression is 7·3=21 and the expanded form is 16+8−3=21. A numerical spot check does not prove an identity, but it often exposes a missing product or sign error before the result is reused.

Solving and simplifying answer different questions

Simplification preserves the value

A simplified expression is another representation of the same function. No particular x is selected. Use the simplify calculator when expanding products and collecting powers is the whole task.

Solving selects admissible inputs

An equation asks which x-values make a statement true. A quadratic can have two, one repeated, or two complex roots; the quadratic formula calculator exposes that classification from a, b, and c.

Factoring exposes multiplication structure

An algebra answer should survive four quick audits

Read the normalized problem and confirm that implicit multiplication, minus signs, parentheses, and powers were interpreted as intended.
Trace every equality as an equivalence, not merely as an instruction to move a term across the page; the underlying justification is an equality property or distribution.
Substitute each proposed solution into the original equation, especially after squaring, clearing denominators, or using a numerical approximation outside this bounded workbench.
Use the system of equations calculator when two or three variables must satisfy several equations simultaneously; a one-variable parser cannot infer that larger model.

Solution steps

Enter your values

Distribute by place, not by memory

Combine only matching powers

Check at a harmless value

Algebra begins by deciding what each symbol is doing

A garden-border expression shows why equivalent is not identical-looking

Solving and simplifying answer different questions

Simplification preserves the value

Solving selects admissible inputs

Factoring exposes multiplication structure

An algebra answer should survive four quick audits

Important limitations

Solution steps

Enter your values

Distribute by place, not by memory

Combine only matching powers

Check at a harmless value

Algebra begins by deciding what each symbol is doing

A garden-border expression shows why equivalent is not identical-looking

Solving and simplifying answer different questions

Simplification preserves the value

Solving selects admissible inputs

Factoring exposes multiplication structure

An algebra answer should survive four quick audits