2*(x+4)*(x+4)=32

Solution for 2*(x+4)*(x+4)=32 equation:

Simplifying
2(x + 4)(x + 4) = 32

Reorder the terms:
2(4 + x)(x + 4) = 32

Reorder the terms:
2(4 + x)(4 + x) = 32

Multiply (4 + x) * (4 + x)
2(4(4 + x) + x(4 + x)) = 32
2((4 * 4 + x * 4) + x(4 + x)) = 32
2((16 + 4x) + x(4 + x)) = 32
2(16 + 4x + (4 * x + x * x)) = 32
2(16 + 4x + (4x + x2)) = 32

Combine like terms: 4x + 4x = 8x
2(16 + 8x + x2) = 32
(16 * 2 + 8x * 2 + x2 * 2) = 32
(32 + 16x + 2x2) = 32

Add '-32' to each side of the equation.
32 + 16x + -32 + 2x2 = 32 + -32

Reorder the terms:
32 + -32 + 16x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
0 + 16x + 2x2 = 32 + -32
16x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
16x + 2x2 = 0

Solving
16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(8 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0, -8}