(x-3)(x+4)-2(3x-2)=(x-4)^2

2 min read Jun 17, 2024

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

This article will guide you through the process of solving the algebraic equation (x-3)(x+4)-2(3x-2)=(x-4)^2. Let's break it down step-by-step.

First, we need to expand the products on both sides of the equation.

Left-hand side:
- (x-3)(x+4) = x² + x - 12 (using the FOIL method)
- -2(3x-2) = -6x + 4
Right-hand side:
- (x-4)² = (x-4)(x-4) = x² - 8x + 16 (using the FOIL method or recognizing the pattern of squaring a binomial)

Now, the equation becomes: x² + x - 12 - 6x + 4 = x² - 8x + 16

Next, combine like terms on both sides of the equation:

Now, we aim to get all the x terms on one side of the equation and the constant terms on the other. Subtract x² from both sides to eliminate it:

Then, add 8x to both sides:

Finally, add 8 to both sides:

Divide both sides by 3 to isolate x:

Therefore, the solution to the equation (x-3)(x+4)-2(3x-2)=(x-4)^2 is x = 8.