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(2x+2)(x-1)-(x+2)(2x+1)=0

2 min read Jun 16, 2024
(2x+2)(x-1)-(x+2)(2x+1)=0

Solving the Equation: (2x+2)(x-1)-(x+2)(2x+1)=0

This article will walk you through the process of solving the algebraic equation: (2x+2)(x-1)-(x+2)(2x+1)=0.

Expanding the Equation

First, we need to expand the equation by multiplying the terms in each set of parentheses.

  • (2x+2)(x-1):
    • 2x * x = 2x²
    • 2x * -1 = -2x
    • 2 * x = 2x
    • 2 * -1 = -2
  • (x+2)(2x+1):
    • x * 2x = 2x²
    • x * 1 = x
    • 2 * 2x = 4x
    • 2 * 1 = 2

Putting these together, our equation becomes:

2x² - 2x + 2x - 2 - (2x² + x + 4x + 2) = 0

Simplifying the Equation

Next, we can simplify the equation by combining like terms:

  • 2x² - 2x² = 0
  • -2x + 2x = 0
  • x + 4x = 5x
  • -2 - 2 = -4

Our simplified equation is now:

-5x - 4 = 0

Solving for x

Finally, we can solve for x:

  1. Add 4 to both sides: -5x = 4
  2. Divide both sides by -5: x = -4/5

Therefore, the solution to the equation (2x+2)(x-1)-(x+2)(2x+1)=0 is x = -4/5.

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