(x-4)(x-6)-(x-2)(x+2)=-2

2 min read Jun 17, 2024

Solving the Equation: (x-4)(x-6)-(x-2)(x+2)=-2

This article will guide you through the process of solving the equation (x-4)(x-6)-(x-2)(x+2)=-2. We will break down each step to make it easy to understand.

Expanding the Equation

First, we need to expand the equation by multiplying the terms in the parentheses:

(x-4)(x-6) = x² - 6x - 4x + 24 = x² - 10x + 24
(x-2)(x+2) = x² + 2x - 2x - 4 = x² - 4

Now our equation becomes: x² - 10x + 24 - (x² - 4) = -2

Simplifying the Equation

Next, we simplify the equation by combining like terms:

x² - x² = 0
-10x remains as -10x
24 + 4 = 28
So the equation becomes: -10x + 28 = -2

Isolating the Variable (x)

Now, we need to isolate the variable 'x' by moving the constant term (28) to the right side of the equation:

-10x = -2 - 28
-10x = -30

Solving for x

Finally, we solve for 'x' by dividing both sides of the equation by -10:

x = -30 / -10
x = 3

Conclusion

Therefore, the solution to the equation (x-4)(x-6)-(x-2)(x+2)=-2 is x = 3.