32=2(x+1)(x+1)

Solution for 32=2(x+1)(x+1) equation:

Simplifying
32 = 2(x + 1)(x + 1)

Reorder the terms:
32 = 2(1 + x)(x + 1)

Reorder the terms:
32 = 2(1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
32 = 2(1(1 + x) + x(1 + x))
32 = 2((1 * 1 + x * 1) + x(1 + x))
32 = 2((1 + 1x) + x(1 + x))
32 = 2(1 + 1x + (1 * x + x * x))
32 = 2(1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
32 = 2(1 + 2x + x2)
32 = (1 * 2 + 2x * 2 + x2 * 2)
32 = (2 + 4x + 2x2)

Solving
32 = 2 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 32 + -2 = 30
30 + -4x + -2x2 = 2 + 4x + 2x2 + -2 + -4x + -2x2

Reorder the terms:
30 + -4x + -2x2 = 2 + -2 + 4x + -4x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
30 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
30 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
30 + -4x + -2x2 = 0 + 2x2 + -2x2
30 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -2x + -1x2) = 0

Factor a trinomial.
2((3 + -1x)(5 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {3, -5}