Free Algebra Calculator with Steps

Enter Your Problem:

Evaluate Examples : 1+2, 2/5+6/7, 2^3 * 2^2 (x+1)(x+2)

Simplify Examples : 2x^2+2y @ x=5, y=3, 3x^2+4y @ x=2, y=4

Crop Image : 5x-3 = 3(x+4), 6x + 5 = 4(x + 7), 3x - 2 = 2(x + 9)

Algebra Calculator:

This algebra calculator helps you solve and understand algebra problems step-by-step. You can use it to simplify expressions, solve equations, and factor polynomials—all in one place, instantly and accurately.

What Problems Can You Solve?

Our free algebra equation solver supports a wide range of algebraic operations, including:

Linear Equations (e.g., ax + b = 0)
Quadratic Equations and Factoring (e.g., ax² + bx + c = 0)
Simplifying Expressions and Factoring Polynomials
Systems of Equations (two or more variables)
Inequalities and Absolute Value Equations

Whether you are a student, teacher, or professional, this math solver makes algebra problems simple and manageable.

Why Use Our Algebra Calculator?

Fast & Free:

Save time and effort by using our calculator. It provides instant and accurate results for all your algebra needs, completely free.

Detailed Step-by-Step Explanations:

Our calculator gives detailed, step-by-step solutions, helping you understand each part of the process. It's perfect for verifying homework, practicing for exams, and building confidence in problem-solving.

Supports Multiple Problem Types:

This all-in-one algebra solver handles a wide range of problems. Whether you need to simplify expressions, factor polynomials, solve linear or quadratic equations, or solve systems of equations, it does it efficiently.

Works on All Smart Devices:

The calculator is fully optimized for PCs, smartphones, tablets, and other devices, delivering a fast and user-friendly experience across all platforms.

How to Use the Algebra Calculator?

Step #1: Type the equation, paste it, or upload an image in the input box
Step #2: Click the "Calculate" button
Step #3: View the result along with detailed steps

💡 Tip:

Use parentheses to clarify the order of operations
Enter one equation per input for accurate results

What is Algebra?

Algebra is a branch of mathematics that uses letters and symbols to represent unknown numbers and solve equations. These letters (such as x, y, and z) are called variables.

The term "algebra" comes from the Arabic word "al-jabr", meaning "reunion of broken parts." The Persian mathematician Al-Khwarizmi is known as the "father of algebra."

How to Solve Algebraic Expressions?

To solve algebraic expressions, follow these steps:

Read the problem carefully and understand the equation
Combine like terms (terms with the same variable and exponent)
Move variables to one side and constants to the other
Simplify and solve to find the variable’s value

Operations with Algebraic Terms

Addition:

Addition applies to like terms only. Like terms have the same variable(s) raised to the same exponent.

Examples:

3x + 5x = 8x
2a + 4b + 3a = 5a + 4b

Subtraction:

Subtract coefficients of like terms while keeping the variable and exponent unchanged.

Examples:

7y - 3y = 4y
6m - 2n - 4m = 2m - 2n

Multiplication:

Multiply the coefficients and apply the laws of exponents to the variables.

Examples:

(3x)(4x) = 12x²
(2a)(3b) = 6ab

Division:

Divide coefficients and subtract exponents of like variables. Different variables remain unchanged.

Examples:

6x³ / 3x = 2x²
10ab / 5a = 2b

How to Solve Basic Algebraic Equations?

One-Step Equations:

Addition/Subtraction: x + 3 = 5 → x = 2

Multiplication/Division: x / 3 = 7 → x = 21

Two-Step Equations:

3x + 5 = 14 → 3x = 9 → x = 3

Multi-Step Equations:

2(x + 3) - 5 = 7 → 2x + 1 = 7 → 2x = 6 → x = 3

Variables on Both Sides:

2x + 3 = x + 9 → x + 3 = 9 → x = 6

Why Learning Algebra Matters?

Algebra develops logical reasoning, problem-solving skills, and understanding of relationships between numbers. Manual calculations can be time-consuming, but an algebra calculator saves time and reduces errors while providing step-by-step explanations for learning purposes.

Benefits for Students & Educators

For Students:

Understand Better: Step-by-step solutions improve problem-solving skills.
Check Homework: Verify answers, identify mistakes, and correct them.
Save Time: Quickly solve problems and complete assignments efficiently.

For Educators:

Enhance Teaching: Demonstrate problem-solving in real time or prepare lectures efficiently.
Support Conceptual Learning: Step-by-step breakdown clarifies complex problems.
Promote Active Learning: Students explore solutions and build independence and confidence.

FAQ

Can the tool solve any algebraic equation?

Yes, it solves equations from simple linear to complex quadratic and beyond.

Is it free and are there limitations?

Yes, it is completely free. Very large or complex equations may take slightly longer to process.

Can it solve systems of equations?

Yes, enter multiple equations separated by a semicolon, e.g., 2x + 3y = 7; x - y = 1. The calculator returns the solution pair (x, y).

What are the 5 basic rules of algebra?

Commutative: a + b = b + a, a × b = b × a
Associative: (a + b) + c = a + (b + c)
Distributive: a(b + c) = ab + ac
Identity: a + 0 = a, a × 1 = a
Inverse: a + (-a) = 0, a × (1/a) = 1

Important Algebraic Formulas

a² - b² = (a - b)(a + b)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
a³ - b³ = (a - b)(a² + ab + b²)
(a + b)³ = a³ + 3a²b + 3ab² + b³

References:

Khan Academy: Solving equations and inequalities
Lumen Learning: Algebraic operations on functions
Wikipedia: Algebra – Definition and etymology

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EN	ES	FR
AR	JA	PL
TH	VI	DE
FI	RU	DA
KO	PT	BN
HI	RO	IT
SV	NL	TR
ID	ZH	EL
CS