In this guide, we'll walk through Algebra Basics — Complete Guide with Examples step by step. Whether you're revising for an exam or practising algebra basics, this clear walkthrough will help you understand not just the answer, but the reasoning behind every step.

Quick Answer

See the step-by-step solution above for the complete answer.

Step-by-Step Solution

Step 1: GCF is 6

Step 2: 12x ÷ 6 = 2x

Step 3: 18 ÷ 6 = 3

Step 4: = 6(2x + 3)

Step 5: Combine like terms: (6+3)x = 9x

Step 6: Combine like terms: (5+4)x = 9x

Step 7: Distribute 3: 3×2x + 3×5 = 6x + 15

Step 8: Distribute 3: 3×6x + 3×4 = 18x + 12

Step 9: GCF is 6

Step 10: 12x ÷ 6 = 2x

Step 11: 18 ÷ 6 = 3

Step 12: = 6(2x + 3)

Step 13: Combine like terms: (2+1)x = 3x

Step 14: Distribute 6: 6×1x + 6×2 = 6x + 12

Step 15: GCF is 4

Step 16: 20x ÷ 4 = 5x

Step 17: 24 ÷ 4 = 6

Step 18: = 4(5x + 6)

Step 19: Combine like terms: (1+1)x = 2x

Step 20: Distribute 3: 3×2x + 3×2 = 6x + 6

Step 21: GCF is 4

Step 22: 16x ÷ 4 = 4x

Step 23: 20 ÷ 4 = 5

Step 24: = 4(4x + 5)

Step 25: Combine like terms: (4+4)x = 8x

Step 26: Distribute 6: 6×5x + 6×5 = 30x + 30

Step 27: GCF is 2

Step 28: 14x ÷ 2 = 7x

Step 29: 16 ÷ 2 = 8

Step 30: = 2(7x + 8)

Step 31: Combine like terms: (7+2)x = 9x

Step 32: Distribute 3: 3×8x + 3×3 = 24x + 9

Step 33: GCF is 5

Step 34: 15x ÷ 5 = 3x

Step 35: 20 ÷ 5 = 4

Step 36: = 5(3x + 4)

Step 37: Combine like terms: (3+5)x = 8x

Step 38: Distribute 6: 6×3x + 6×1 = 18x + 6

Step 39: GCF is 3

Step 40: 18x ÷ 3 = 6x

Step 41: 21 ÷ 3 = 7

Step 42: = 3(6x + 7)

Why This Works

This problem uses algebra basics. The key idea is to perform the same operation on both sides to keep the equation balanced. Each step brings you closer to isolating the unknown variable.

Common Mistakes to Avoid

❌ Mistake 1: Forgetting to apply the same operation to both sides of the equation.

❌ Mistake 2: Making sign errors when moving terms across the equals sign.

❌ Mistake 3: Not simplifying the final answer completely.

Practice Similar Problems

• Solve: x² + 9x + 0 = 0
• Solve: x² + 11x - 12 = 0
• Solve: x² - 6x + 9 = 0
• Solve: x² + 12x + 32 = 0
• Solve: x² + 6x - 72 = 0

Frequently Asked Questions