-12x^2+28x-6=0

Solution for -12x^2+28x-6=0 equation:

Simplifying
-12x2 + 28x + -6 = 0

Reorder the terms:
-6 + 28x + -12x2 = 0

Solving
-6 + 28x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 14x + -6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 14x + -6x2)' equal to zero and attempt to solve:

Simplifying
-3 + 14x + -6x2 = 0

Solving
-3 + 14x + -6x2 = 0

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

Divide each side by '-6'.
0.5 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2.333333333x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2.333333333x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2.333333333x + x2 = 0 + -0.5
-2.333333333x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2.333333333x + x2 = -0.5

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -0.5 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -0.5 + 1.361111112

Combine like terms: -0.5 + 1.361111112 = 0.861111112
1.361111112 + -2.333333333x + x2 = 0.861111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 0.861111112

Calculate the square root of the right side: 0.927960728

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 0.927960728 and -0.927960728.

Subproblem 1
x + -1.166666667 = 0.927960728

Simplifying
x + -1.166666667 = 0.927960728

Reorder the terms:
-1.166666667 + x = 0.927960728

Solving
-1.166666667 + x = 0.927960728

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 0.927960728 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 0.927960728 + 1.166666667
x = 0.927960728 + 1.166666667

Combine like terms: 0.927960728 + 1.166666667 = 2.094627395
x = 2.094627395

Simplifying
x = 2.094627395

Subproblem 2
x + -1.166666667 = -0.927960728

Simplifying
x + -1.166666667 = -0.927960728

Reorder the terms:
-1.166666667 + x = -0.927960728

Solving
-1.166666667 + x = -0.927960728

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -0.927960728 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -0.927960728 + 1.166666667
x = -0.927960728 + 1.166666667

Combine like terms: -0.927960728 + 1.166666667 = 0.238705939
x = 0.238705939

Simplifying
x = 0.238705939

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.094627395, 0.238705939}
Solution
x = {2.094627395, 0.238705939}