2(x-2)(x-2)-8=24

Solution for 2(x-2)(x-2)-8=24 equation:

Simplifying
2(x + -2)(x + -2) + -8 = 24

Reorder the terms:
2(-2 + x)(x + -2) + -8 = 24

Reorder the terms:
2(-2 + x)(-2 + x) + -8 = 24

Multiply (-2 + x) * (-2 + x)
2(-2(-2 + x) + x(-2 + x)) + -8 = 24
2((-2 * -2 + x * -2) + x(-2 + x)) + -8 = 24
2((4 + -2x) + x(-2 + x)) + -8 = 24
2(4 + -2x + (-2 * x + x * x)) + -8 = 24
2(4 + -2x + (-2x + x2)) + -8 = 24

Combine like terms: -2x + -2x = -4x
2(4 + -4x + x2) + -8 = 24
(4 * 2 + -4x * 2 + x2 * 2) + -8 = 24
(8 + -8x + 2x2) + -8 = 24

Reorder the terms:
8 + -8 + -8x + 2x2 = 24

Combine like terms: 8 + -8 = 0
0 + -8x + 2x2 = 24
-8x + 2x2 = 24

Solving
-8x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -8x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -4x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}