10x^2-72x+12=0

Solution for 10x^2-72x+12=0 equation:

Simplifying
10x2 + -72x + 12 = 0

Reorder the terms:
12 + -72x + 10x2 = 0

Solving
12 + -72x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -36x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -36x + 5x2)' equal to zero and attempt to solve:

Simplifying
6 + -36x + 5x2 = 0

Solving
6 + -36x + 5x2 = 0

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

Divide each side by '5'.
1.2 + -7.2x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -7.2x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -7.2x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -7.2x + x2 = 0 + -1.2
-7.2x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-7.2x + x2 = -1.2

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = -1.2 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = -1.2 + 12.96

Combine like terms: -1.2 + 12.96 = 11.76
12.96 + -7.2x + x2 = 11.76

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 11.76

Calculate the square root of the right side: 3.42928564

Break this problem into two subproblems by setting 
(x + -3.6) equal to 3.42928564 and -3.42928564.

Subproblem 1
x + -3.6 = 3.42928564

Simplifying
x + -3.6 = 3.42928564

Reorder the terms:
-3.6 + x = 3.42928564

Solving
-3.6 + x = 3.42928564

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = 3.42928564 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = 3.42928564 + 3.6
x = 3.42928564 + 3.6

Combine like terms: 3.42928564 + 3.6 = 7.02928564
x = 7.02928564

Simplifying
x = 7.02928564

Subproblem 2
x + -3.6 = -3.42928564

Simplifying
x + -3.6 = -3.42928564

Reorder the terms:
-3.6 + x = -3.42928564

Solving
-3.6 + x = -3.42928564

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = -3.42928564 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = -3.42928564 + 3.6
x = -3.42928564 + 3.6

Combine like terms: -3.42928564 + 3.6 = 0.17071436
x = 0.17071436

Simplifying
x = 0.17071436

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.02928564, 0.17071436}
Solution
x = {7.02928564, 0.17071436}