2(x^2+4x+4)-32=0

Solution for 2(x^2+4x+4)-32=0 equation:

Simplifying
2(x2 + 4x + 4) + -32 = 0

Reorder the terms:
2(4 + 4x + x2) + -32 = 0
(4 * 2 + 4x * 2 + x2 * 2) + -32 = 0
(8 + 8x + 2x2) + -32 = 0

Reorder the terms:
8 + -32 + 8x + 2x2 = 0

Combine like terms: 8 + -32 = -24
-24 + 8x + 2x2 = 0

Solving
-24 + 8x + 2x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 2}