(x+3)(x-2)-(x+4)(x-1)=3x

2 min read Jun 16, 2024

Solving the Equation: (x+3)(x-2)-(x+4)(x-1)=3x

This article will guide you through the steps of solving the equation (x+3)(x-2)-(x+4)(x-1)=3x. We will use algebraic manipulation to isolate the variable 'x' and find its value.

Expanding the Equation

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

(x+3)(x-2) = x² + x - 6
(x+4)(x-1) = x² + 3x - 4

Now, the equation becomes: (x² + x - 6) - (x² + 3x - 4) = 3x

Simplifying the Equation

Next, we can simplify the equation by combining like terms:

x² - x² + x - 3x - 6 + 4 = 3x
-2x - 2 = 3x

Isolate the Variable

To isolate the variable 'x', we can move all the 'x' terms to one side of the equation and the constants to the other:

-2x - 3x = 2
-5x = 2

Solving for x

Finally, we can solve for 'x' by dividing both sides of the equation by -5:

x = -2/5

Therefore, the solution to the equation (x+3)(x-2)-(x+4)(x-1)=3x is x = -2/5.