(3x-1)^2-5(2x+1)^2+(6x-3)(2x+1)=(x-1)^2

2 min read Jun 16, 2024

Solving the Equation: (3x-1)^2-5(2x+1)^2+(6x-3)(2x+1)=(x-1)^2

This article will guide you through the process of solving the given equation:

(3x-1)^2-5(2x+1)^2+(6x-3)(2x+1)=(x-1)^2

1. Expanding the Equation

First, we need to expand the squares and the product of the binomials:

Now, substitute these expanded terms back into the original equation:

9x^2 - 6x + 1 - 5(4x^2 + 4x + 1) + 12x^2 - 3 = x^2 - 2x + 1

2. Simplifying the Equation

Next, distribute the -5 and simplify the equation:

9x^2 - 6x + 1 - 20x^2 - 20x - 5 + 12x^2 - 3 = x^2 - 2x + 1

x^2 - 24x - 6 = x^2 - 2x + 1

3. Solving for x

To solve for x, we need to isolate the x terms on one side and the constant terms on the other:

x^2 - 24x - x^2 + 2x = 1 + 6

-22x = 7

x = -7/22

Therefore, the solution to the equation (3x-1)^2-5(2x+1)^2+(6x-3)(2x+1)=(x-1)^2 is x = -7/22.