6x^2-2x-12=12

Solution for 6x^2-2x-12=12 equation:

Simplifying
6x2 + -2x + -12 = 12

Reorder the terms:
-12 + -2x + 6x2 = 12

Solving
-12 + -2x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -12 + -2x + 6x2 = 12 + -12

Combine like terms: -12 + -12 = -24
-24 + -2x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-24 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
-12 + -1x + 3x2 = 0

Solving
-12 + -1x + 3x2 = 0

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

Divide each side by '3'.
-4 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.3333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.3333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.3333333333x + x2 = 0 + 4
-0.3333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.3333333333x + x2 = 4

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 4 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 4 + 0.02777777779

Combine like terms: 4 + 0.02777777779 = 4.02777777779
0.02777777779 + -0.3333333333x + x2 = 4.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 4.02777777779

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 2.00693243 and -2.00693243.

Subproblem 1
x + -0.1666666667 = 2.00693243

Simplifying
x + -0.1666666667 = 2.00693243

Reorder the terms:
-0.1666666667 + x = 2.00693243

Solving
-0.1666666667 + x = 2.00693243

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 2.00693243 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 2.00693243 + 0.1666666667
x = 2.00693243 + 0.1666666667

Combine like terms: 2.00693243 + 0.1666666667 = 2.1735990967
x = 2.1735990967

Simplifying
x = 2.1735990967

Subproblem 2
x + -0.1666666667 = -2.00693243

Simplifying
x + -0.1666666667 = -2.00693243

Reorder the terms:
-0.1666666667 + x = -2.00693243

Solving
-0.1666666667 + x = -2.00693243

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -2.00693243 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -2.00693243 + 0.1666666667
x = -2.00693243 + 0.1666666667

Combine like terms: -2.00693243 + 0.1666666667 = -1.8402657633
x = -1.8402657633

Simplifying
x = -1.8402657633

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1735990967, -1.8402657633}
Solution
x = {2.1735990967, -1.8402657633}