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(x-4)(x-6)=(x+2)(x-8)

less than a minute read Jun 17, 2024
(x-4)(x-6)=(x+2)(x-8)

Solving the Equation: (x-4)(x-6) = (x+2)(x-8)

This equation involves expanding both sides and then solving for x. Let's break it down step-by-step:

1. Expanding Both Sides

  • Left Side: (x-4)(x-6) = x(x-6) - 4(x-6) = x² - 6x - 4x + 24 = x² - 10x + 24

  • Right Side: (x+2)(x-8) = x(x-8) + 2(x-8) = x² - 8x + 2x - 16 = x² - 6x - 16

2. Setting the Equations Equal

Now we have: x² - 10x + 24 = x² - 6x - 16

3. Simplifying and Solving

  • Subtract x² from both sides: -10x + 24 = -6x - 16
  • Add 6x to both sides: -4x + 24 = -16
  • Subtract 24 from both sides: -4x = -40
  • Divide both sides by -4: x = 10

Solution

Therefore, the solution to the equation (x-4)(x-6) = (x+2)(x-8) is x = 10.

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