(x^2-2x)-(-3x-6)=8

Solution for (x^2-2x)-(-3x-6)=8 equation:

Simplifying
(x2 + -2x) + -1(-3x + -6) = 8

Reorder the terms:
(-2x + x2) + -1(-3x + -6) = 8

Remove parenthesis around (-2x + x2)
-2x + x2 + -1(-3x + -6) = 8

Reorder the terms:
-2x + x2 + -1(-6 + -3x) = 8
-2x + x2 + (-6 * -1 + -3x * -1) = 8
-2x + x2 + (6 + 3x) = 8

Reorder the terms:
6 + -2x + 3x + x2 = 8

Combine like terms: -2x + 3x = 1x
6 + 1x + x2 = 8

Solving
6 + 1x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
6 + -8 + 1x + x2 = 8 + -8

Combine like terms: 6 + -8 = -2
-2 + 1x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-2 + 1x + x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-2, 1}