6x^2-60x+36=0

Solution for 6x^2-60x+36=0 equation:

Simplifying
6x2 + -60x + 36 = 0

Reorder the terms:
36 + -60x + 6x2 = 0

Solving
36 + -60x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -10x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -10x + x2 = 0

Solving
6 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -10x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -10x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -10x + x2 = 0 + -6
-10x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-10x + x2 = -6

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -6 + 25

Reorder the terms:
25 + -10x + x2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + -10x + x2 = 19

Factor a perfect square on the left side:
(x + -5)(x + -5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -5) equal to 4.358898944 and -4.358898944.

Subproblem 1
x + -5 = 4.358898944

Simplifying
x + -5 = 4.358898944

Reorder the terms:
-5 + x = 4.358898944

Solving
-5 + x = 4.358898944

Solving for variable 'x'.

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 = 4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.358898944 + 5
x = 4.358898944 + 5

Combine like terms: 4.358898944 + 5 = 9.358898944
x = 9.358898944

Simplifying
x = 9.358898944

Subproblem 2
x + -5 = -4.358898944

Simplifying
x + -5 = -4.358898944

Reorder the terms:
-5 + x = -4.358898944

Solving
-5 + x = -4.358898944

Solving for variable 'x'.

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 = -4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.358898944 + 5
x = -4.358898944 + 5

Combine like terms: -4.358898944 + 5 = 0.641101056
x = 0.641101056

Simplifying
x = 0.641101056

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.358898944, 0.641101056}
Solution
x = {9.358898944, 0.641101056}