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(x-6)(x+7)=(x+3)(x-11)

2 min read Jun 17, 2024
(x-6)(x+7)=(x+3)(x-11)

Solving the Equation: (x-6)(x+7) = (x+3)(x-11)

This equation involves expanding brackets and simplifying to solve for the unknown variable 'x'. Let's break down the process step by step.

Expanding the Brackets

First, we expand the brackets on both sides of the equation using the distributive property (also known as FOIL method).

  • Left side: (x-6)(x+7) = x(x+7) - 6(x+7) = x² + 7x - 6x - 42 = x² + x - 42
  • Right side: (x+3)(x-11) = x(x-11) + 3(x-11) = x² - 11x + 3x - 33 = x² - 8x - 33

Now, our equation becomes: x² + x - 42 = x² - 8x - 33

Simplifying the Equation

To simplify, we can move all terms to one side of the equation:

  • Subtract x² from both sides: x - 42 = -8x - 33
  • Add 8x to both sides: 9x - 42 = -33
  • Add 42 to both sides: 9x = 9

Solving for x

Finally, we isolate 'x' by dividing both sides by 9:

  • x = 1

Therefore, the solution to the equation (x-6)(x+7) = (x+3)(x-11) is x = 1.

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