(x+1)(x+4)=(x-7)(x+6)

Jasonbradley

2 min read

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Jun 16, 2024

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Solving the Equation (x+1)(x+4) = (x-7)(x+6)

This equation involves expanding both sides and then solving for the value of x. Let's break down the steps:

1. Expand both sides of the equation:

• Left side:
  • (x+1)(x+4) = x(x+4) + 1(x+4) = x² + 4x + x + 4 = x² + 5x + 4
• Right side:
  • (x-7)(x+6) = x(x+6) - 7(x+6) = x² + 6x - 7x - 42 = x² - x - 42

Now, our equation becomes: x² + 5x + 4 = x² - x - 42

2. Simplify the equation:

• Subtract x² from both sides: 5x + 4 = -x - 42
• Add x to both sides: 6x + 4 = -42
• Subtract 4 from both sides: 6x = -46

3. Solve for x:

• Divide both sides by 6: x = -46/6
• Simplify the fraction: x = -23/3

Therefore, the solution to the equation (x+1)(x+4) = (x-7)(x+6) is x = -23/3.