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

2 min read Jun 16, 2024

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

This article will guide you through the process of solving the equation (2x+1)^2 - 3(x-5)^2 = (x+3)(x-3).

The first step is to expand the squares and the product on both sides of the equation.

Left side:
- (2x+1)^2 = (2x+1)(2x+1) = 4x^2 + 4x + 1
- 3(x-5)^2 = 3(x-5)(x-5) = 3(x^2 -10x + 25) = 3x^2 - 30x + 75
Right side:
- (x+3)(x-3) = x^2 - 9

Substituting these expanded forms into the original equation gives us:

4x^2 + 4x + 1 - (3x^2 - 30x + 75) = x^2 - 9

Now, we simplify the equation by combining like terms:

4x^2 + 4x + 1 - 3x^2 + 30x - 75 = x^2 - 9

x^2 + 34x - 74 = x^2 - 9

Further simplification leads to:

34x - 74 = -9

34x = 65

x = 65/34

Therefore, the solution to the equation (2x+1)^2 - 3(x-5)^2 = (x+3)(x-3) is x = 65/34.