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

2 min read Jun 17, 2024
(x-1)(x+6)-(x-2)(x-3)=3

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

This article will guide you through the steps of solving the equation (x-1)(x+6)-(x-2)(x-3)=3.

Expanding the Equation

First, we need to expand the equation by multiplying out the brackets:

  • (x-1)(x+6) = x² + 6x - x - 6 = x² + 5x - 6
  • (x-2)(x-3) = x² - 3x - 2x + 6 = x² - 5x + 6

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

x² + 5x - 6 - (x² - 5x + 6) = 3

Simplifying the Equation

Next, we simplify the equation by removing the parentheses and combining like terms:

x² + 5x - 6 - x² + 5x - 6 = 3 10x - 12 = 3

Isolating the Variable

To solve for 'x', we need to isolate the variable by adding 12 to both sides of the equation:

10x = 15

Solving for 'x'

Finally, we divide both sides of the equation by 10 to get the solution for 'x':

x = 15/10 x = 1.5

Therefore, the solution to the equation (x-1)(x+6)-(x-2)(x-3)=3 is x = 1.5.