6x^2-48x+12=0

Solution for 6x^2-48x+12=0 equation:

Simplifying
6x2 + -48x + 12 = 0

Reorder the terms:
12 + -48x + 6x2 = 0

Solving
12 + -48x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -8x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -8x + x2 = 0

Solving
2 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -8x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -8x + x2 = 0 + -2

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -2 + 16

Reorder the terms:
16 + -8x + x2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + -8x + x2 = 14

Factor a perfect square on the left side:
(x + -4)(x + -4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -4) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + -4 = 3.741657387

Simplifying
x + -4 = 3.741657387

Reorder the terms:
-4 + x = 3.741657387

Solving
-4 + x = 3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.741657387 + 4
x = 3.741657387 + 4

Combine like terms: 3.741657387 + 4 = 7.741657387
x = 7.741657387

Simplifying
x = 7.741657387

Subproblem 2
x + -4 = -3.741657387

Simplifying
x + -4 = -3.741657387

Reorder the terms:
-4 + x = -3.741657387

Solving
-4 + x = -3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.741657387 + 4
x = -3.741657387 + 4

Combine like terms: -3.741657387 + 4 = 0.258342613
x = 0.258342613

Simplifying
x = 0.258342613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.741657387, 0.258342613}
Solution
x = {7.741657387, 0.258342613}