(2x+6)(2x-6)=(2x+9)(3x-4)

2 min read Jun 16, 2024

Solving the Equation: (2x+6)(2x-6) = (2x+9)(3x-4)

This article will guide you through the steps of solving the equation (2x+6)(2x-6) = (2x+9)(3x-4).

Expanding the Equation

First, we need to expand both sides of the equation using the FOIL method (First, Outer, Inner, Last) or by simply multiplying each term in the first bracket by each term in the second bracket.

Left side: (2x+6)(2x-6) = 4x² - 12x + 12x - 36 = 4x² - 36
Right side: (2x+9)(3x-4) = 6x² - 8x + 27x - 36 = 6x² + 19x - 36

Now our equation becomes: 4x² - 36 = 6x² + 19x - 36

Rearranging the Equation

To solve for x, we need to bring all the terms to one side of the equation. Subtracting 4x² and adding 36 to both sides, we get:

0 = 2x² + 19x

Solving the Quadratic Equation

We now have a quadratic equation in the form ax² + bx + c = 0. In this case, a = 2, b = 19, and c = 0.

We can solve this equation by factoring:

Factor out x: 0 = x(2x + 19)
Set each factor to zero:
- x = 0
- 2x + 19 = 0
Solve for x:
- x = 0
- x = -19/2

Solution

Therefore, the solutions to the equation (2x+6)(2x-6) = (2x+9)(3x-4) are x = 0 and x = -19/2.