(2(x-12))(2(x-12))=72

Solution for (2(x-12))(2(x-12))=72 equation:

Simplifying
(2(x + -12))(2(x + -12)) = 72

Reorder the terms:
(2(-12 + x))(2(x + -12)) = 72
((-12 * 2 + x * 2))(2(x + -12)) = 72
((-24 + 2x))(2(x + -12)) = 72

Reorder the terms:
(-24 + 2x)(2(-12 + x)) = 72
(-24 + 2x)((-12 * 2 + x * 2)) = 72
(-24 + 2x)((-24 + 2x)) = 72

Multiply (-24 + 2x) * (-24 + 2x)
(-24(-24 + 2x) + 2x * (-24 + 2x)) = 72
((-24 * -24 + 2x * -24) + 2x * (-24 + 2x)) = 72
((576 + -48x) + 2x * (-24 + 2x)) = 72
(576 + -48x + (-24 * 2x + 2x * 2x)) = 72
(576 + -48x + (-48x + 4x2)) = 72

Combine like terms: -48x + -48x = -96x
(576 + -96x + 4x2) = 72

Solving
576 + -96x + 4x2 = 72

Solving for variable 'x'.

Reorder the terms:
576 + -72 + -96x + 4x2 = 72 + -72

Combine like terms: 576 + -72 = 504
504 + -96x + 4x2 = 72 + -72

Combine like terms: 72 + -72 = 0
504 + -96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(126 + -24x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(126 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
126 + -24x + x2 = 0

Solving
126 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-126' to each side of the equation.
126 + -24x + -126 + x2 = 0 + -126

Reorder the terms:
126 + -126 + -24x + x2 = 0 + -126

Combine like terms: 126 + -126 = 0
0 + -24x + x2 = 0 + -126
-24x + x2 = 0 + -126

Combine like terms: 0 + -126 = -126
-24x + x2 = -126

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -126 + 144

Reorder the terms:
144 + -24x + x2 = -126 + 144

Combine like terms: -126 + 144 = 18
144 + -24x + x2 = 18

Factor a perfect square on the left side:
(x + -12)(x + -12) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -12) equal to 4.242640687 and -4.242640687.

Subproblem 1
x + -12 = 4.242640687

Simplifying
x + -12 = 4.242640687

Reorder the terms:
-12 + x = 4.242640687

Solving
-12 + x = 4.242640687

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 4.242640687 + 12

Combine like terms: -12 + 12 = 0
0 + x = 4.242640687 + 12
x = 4.242640687 + 12

Combine like terms: 4.242640687 + 12 = 16.242640687
x = 16.242640687

Simplifying
x = 16.242640687

Subproblem 2
x + -12 = -4.242640687

Simplifying
x + -12 = -4.242640687

Reorder the terms:
-12 + x = -4.242640687

Solving
-12 + x = -4.242640687

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -4.242640687 + 12

Combine like terms: -12 + 12 = 0
0 + x = -4.242640687 + 12
x = -4.242640687 + 12

Combine like terms: -4.242640687 + 12 = 7.757359313
x = 7.757359313

Simplifying
x = 7.757359313

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.242640687, 7.757359313}
Solution
x = {16.242640687, 7.757359313}