12x^2-16x-6=0

Solution for 12x^2-16x-6=0 equation:

Simplifying
12x2 + -16x + -6 = 0

Reorder the terms:
-6 + -16x + 12x2 = 0

Solving
-6 + -16x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -8x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -8x + 6x2)' equal to zero and attempt to solve:

Simplifying
-3 + -8x + 6x2 = 0

Solving
-3 + -8x + 6x2 = 0

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

Divide each side by '6'.
-0.5 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.333333333x + x2 = 0 + 0.5
-1.333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.333333333x + x2 = 0.5

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 0.5 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.5 + 0.4444444442

Combine like terms: 0.5 + 0.4444444442 = 0.9444444442
0.4444444442 + -1.333333333x + x2 = 0.9444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.9444444442

Calculate the square root of the right side: 0.971825316

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.971825316 and -0.971825316.

Subproblem 1
x + -0.6666666665 = 0.971825316

Simplifying
x + -0.6666666665 = 0.971825316

Reorder the terms:
-0.6666666665 + x = 0.971825316

Solving
-0.6666666665 + x = 0.971825316

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 0.971825316 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 0.971825316 + 0.6666666665
x = 0.971825316 + 0.6666666665

Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825
x = 1.6384919825

Simplifying
x = 1.6384919825

Subproblem 2
x + -0.6666666665 = -0.971825316

Simplifying
x + -0.6666666665 = -0.971825316

Reorder the terms:
-0.6666666665 + x = -0.971825316

Solving
-0.6666666665 + x = -0.971825316

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -0.971825316 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -0.971825316 + 0.6666666665
x = -0.971825316 + 0.6666666665

Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495
x = -0.3051586495

Simplifying
x = -0.3051586495

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6384919825, -0.3051586495}
Solution
x = {1.6384919825, -0.3051586495}