Solve algebra problems instantly with our free Algebra Calculator. Handle linear equations, quadratic equations, systems of equations, and expression simplification with detailed step-by-step solutions. Perfect for students, teachers, and anyone needing quick algebraic calculations. Get accurate results with work shown for better understanding.

How to Use the Algebra Calculator

Overview

This comprehensive algebra calculator includes four powerful tools: Linear Equation Solver, Quadratic Equation Solver, System of Equations Solver, and Expression Simplifier.

1. LINEAR EQUATION SOLVER

Solves equations in the form: ax + b = c

Steps:

1. Click the “Linear Equation” tab
2. Enter the coefficient a (the number before x)
3. Enter the constant b (added/subtracted term)
4. Enter the result c (what the equation equals)
5. Click “Solve” to get the answer
6. View the solution with step-by-step work

Example:

Solve: 2x + 5 = 11

• a = 2
• b = 5
• c = 11
• Solution: x = 3

Steps shown:

1. 2x + 5 = 11
2. 2x = 11 – 5
3. 2x = 6
4. x = 6 / 2
5. x = 3

2. QUADRATIC EQUATION SOLVER

Solves equations in the form: ax² + bx + c = 0

Steps:

1. Click the “Quadratic” tab
2. Enter coefficient a (before x²)
3. Enter coefficient b (before x)
4. Enter constant c
5. Click “Solve”
6. View solutions (can be 0, 1, or 2 real solutions)

Example:

Solve: x² – 5x + 6 = 0

• a = 1
• b = -5
• c = 6
• Solutions: x₁ = 3, x₂ = 2

Result Types:

• Two solutions: When discriminant > 0
• One solution: When discriminant = 0 (repeated root)
• No real solutions: When discriminant < 0 (complex roots)

3. SYSTEM OF EQUATIONS SOLVER

Solves 2×2 systems:

• Equation 1: a₁x + b₁y = c₁
• Equation 2: a₂x + b₂y = c₂

Steps:

1. Click the “System of Equations” tab
2. Enter coefficients for Equation 1: a₁, b₁, c₁
3. Enter coefficients for Equation 2: a₂, b₂, c₂
4. Click “Solve”
5. View both x and y values with verification

Example:

Solve the system:

• 2x + 3y = 8
• x – y = 1

Input:

• a₁ = 2, b₁ = 3, c₁ = 8
• a₂ = 1, b₂ = -1, c₂ = 1

Solution: x = 2.2, y = 1.2

Note:

If the system has no unique solution (parallel or coincident lines), an error message will appear.

4. EXPRESSION SIMPLIFIER

Currently supports: (a + b)(c + d) expansion

Steps:

1. Click the “Simplify” tab
2. Select operation type (currently: expand binomials)
3. Enter values for a, b, c, and d
4. Click “Simplify”
5. View expanded form with FOIL method breakdown

Example:

Expand: (2 + 3)(1 + 4)

• a = 2, b = 3, c = 1, d = 4
• Result: 20

FOIL Method shown:

• First: 2 × 1 = 2
• Outer: 2 × 4 = 8
• Inner: 3 × 1 = 3
• Last: 3 × 4 = 12
• Sum: 2 + 8 + 3 + 12 = 25

General Features

Clear Button

• Resets all input fields to blank
• Clears the result display
• Allows you to start a new calculation

Step-by-Step Solutions

Every calculation shows:

• The final answer
• Detailed steps of how the solution was reached
• Verification (for systems of equations)
• Formulas used

Error Handling

The calculator alerts you if:

• Required fields are empty
• Invalid numbers are entered
• Division by zero would occur
• No solution exists

Common Use Cases

For Students:

• Homework verification
• Learning equation-solving methods
• Understanding step-by-step processes
• Practice and self-study

For Teachers:

• Creating example problems
• Verifying answer keys
• Demonstrating solving techniques
• Quick calculations during lessons

For Professionals:

• Engineering calculations
• Financial modeling
• Scientific computations
• Quick problem-solving

Tips for Best Results

1. Double-check your inputs before clicking Solve
2. Use the Clear button between different problems
3. Review the steps to understand the solving process
4. For quadratic equations, note whether solutions are real or complex
5. For systems, ensure equations are properly formatted

Supported Equation Types

✅ Linear equations (first degree) ✅ Quadratic equations (second degree) ✅ 2×2 Systems of linear equations ✅ Binomial expansion using FOIL method