(x+2)(x-2)-(2x+1)^2=x(2-3x)

Jasonbradley

2 min read

·

Jun 16, 2024

27

Share

Solving the Equation: (x+2)(x-2)-(2x+1)^2=x(2-3x)

This article will guide you through the steps to solve the given equation: (x+2)(x-2)-(2x+1)^2=x(2-3x). We'll break down the process, making it easy to understand.

Expanding and Simplifying

1. Expand the products:

   • (x+2)(x-2) is a difference of squares: (x+2)(x-2) = x² - 2² = x² - 4
   • (2x+1)² is a perfect square trinomial: (2x+1)² = (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1

   The equation now becomes: x² - 4 - (4x² + 4x + 1) = x(2-3x)

2. Distribute on the right side:

   • x(2-3x) = 2x - 3x²

   Our equation is now: x² - 4 - (4x² + 4x + 1) = 2x - 3x²

3. Remove the parentheses and combine like terms:

   • x² - 4 - 4x² - 4x - 1 = 2x - 3x²
   • -3x² - 4x - 5 = 2x - 3x²

4. Move all terms to one side:

   • -4x - 5 - 2x = 0
   • -6x - 5 = 0

Solving for x

1. Isolate the x term:

   • -6x = 5

2. Divide both sides by -6:

   • x = -5/6

Solution

Therefore, the solution to the equation (x+2)(x-2)-(2x+1)^2=x(2-3x) is x = -5/6.