2(x+2)(x+2)=72

Solution for 2(x+2)(x+2)=72 equation:

Simplifying
2(x + 2)(x + 2) = 72

Reorder the terms:
2(2 + x)(x + 2) = 72

Reorder the terms:
2(2 + x)(2 + x) = 72

Multiply (2 + x) * (2 + x)
2(2(2 + x) + x(2 + x)) = 72
2((2 * 2 + x * 2) + x(2 + x)) = 72
2((4 + 2x) + x(2 + x)) = 72
2(4 + 2x + (2 * x + x * x)) = 72
2(4 + 2x + (2x + x2)) = 72

Combine like terms: 2x + 2x = 4x
2(4 + 4x + x2) = 72
(4 * 2 + 4x * 2 + x2 * 2) = 72
(8 + 8x + 2x2) = 72

Solving
8 + 8x + 2x2 = 72

Solving for variable 'x'.

Reorder the terms:
8 + -72 + 8x + 2x2 = 72 + -72

Combine like terms: 8 + -72 = -64
-64 + 8x + 2x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-64 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}