=12x^2-72x+72

Solution for =12x^2-72x+72 equation:

Simplifying
0 = 12x2 + -72x + 72

Reorder the terms:
0 = 72 + -72x + 12x2

Solving
0 = 72 + -72x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -72 = -72
-72 + 72x + -12x2 = 72 + -72x + 12x2 + -72 + 72x + -12x2

Reorder the terms:
-72 + 72x + -12x2 = 72 + -72 + -72x + 72x + 12x2 + -12x2

Combine like terms: 72 + -72 = 0
-72 + 72x + -12x2 = 0 + -72x + 72x + 12x2 + -12x2
-72 + 72x + -12x2 = -72x + 72x + 12x2 + -12x2

Combine like terms: -72x + 72x = 0
-72 + 72x + -12x2 = 0 + 12x2 + -12x2
-72 + 72x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-72 + 72x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-6 + 6x + -1x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-6 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + 6x + -1x2 = 0

Solving
-6 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -6x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -6x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -6x + x2 = 0 + -6
-6x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-6x + x2 = -6

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -6 + 9

Reorder the terms:
9 + -6x + x2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + -6x + x2 = 3

Factor a perfect square on the left side:
(x + -3)(x + -3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -3 = 1.732050808

Simplifying
x + -3 = 1.732050808

Reorder the terms:
-3 + x = 1.732050808

Solving
-3 + x = 1.732050808

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.732050808 + 3
x = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
x = 4.732050808

Simplifying
x = 4.732050808

Subproblem 2
x + -3 = -1.732050808

Simplifying
x + -3 = -1.732050808

Reorder the terms:
-3 + x = -1.732050808

Solving
-3 + x = -1.732050808

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.732050808 + 3
x = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
x = 1.267949192

Simplifying
x = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.732050808, 1.267949192}
Solution
x = {4.732050808, 1.267949192}