0=12x^2-20x-6

Solution for 0=12x^2-20x-6 equation:

Simplifying
0 = 12x2 + -20x + -6

Reorder the terms:
0 = -6 + -20x + 12x2

Solving
0 = -6 + -20x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 20x + -12x2 = -6 + -20x + 12x2 + 6 + 20x + -12x2

Reorder the terms:
6 + 20x + -12x2 = -6 + 6 + -20x + 20x + 12x2 + -12x2

Combine like terms: -6 + 6 = 0
6 + 20x + -12x2 = 0 + -20x + 20x + 12x2 + -12x2
6 + 20x + -12x2 = -20x + 20x + 12x2 + -12x2

Combine like terms: -20x + 20x = 0
6 + 20x + -12x2 = 0 + 12x2 + -12x2
6 + 20x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
6 + 20x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 10x + -6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 10x + -6x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + -6x2 = 0

Solving
3 + 10x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.5 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.666666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.666666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.666666667x + x2 = 0 + 0.5
-1.666666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.666666667x + x2 = 0.5

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 0.5 + 0.6944444447

Combine like terms: 0.5 + 0.6944444447 = 1.1944444447
0.6944444447 + -1.666666667x + x2 = 1.1944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 1.1944444447

Calculate the square root of the right side: 1.092906421

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.092906421 and -1.092906421.

Subproblem 1
x + -0.8333333335 = 1.092906421

Simplifying
x + -0.8333333335 = 1.092906421

Reorder the terms:
-0.8333333335 + x = 1.092906421

Solving
-0.8333333335 + x = 1.092906421

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.092906421 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.092906421 + 0.8333333335
x = 1.092906421 + 0.8333333335

Combine like terms: 1.092906421 + 0.8333333335 = 1.9262397545
x = 1.9262397545

Simplifying
x = 1.9262397545

Subproblem 2
x + -0.8333333335 = -1.092906421

Simplifying
x + -0.8333333335 = -1.092906421

Reorder the terms:
-0.8333333335 + x = -1.092906421

Solving
-0.8333333335 + x = -1.092906421

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.092906421 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.092906421 + 0.8333333335
x = -1.092906421 + 0.8333333335

Combine like terms: -1.092906421 + 0.8333333335 = -0.2595730875
x = -0.2595730875

Simplifying
x = -0.2595730875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9262397545, -0.2595730875}
Solution
x = {1.9262397545, -0.2595730875}