6x^2-4x-6=0

Solution for 6x^2-4x-6=0 equation:

Simplifying
6x2 + -4x + -6 = 0

Reorder the terms:
-6 + -4x + 6x2 = 0

Solving
-6 + -4x + 6x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-3 + -2x + 3x2 = 0

Solving
-3 + -2x + 3x2 = 0

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

Divide each side by '3'.
-1 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.6666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.6666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.6666666667x + x2 = 0 + 1
-0.6666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.6666666667x + x2 = 1

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + -0.6666666667x + x2 = 1.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.054092553 and -1.054092553.

Subproblem 1
x + -0.3333333334 = 1.054092553

Simplifying
x + -0.3333333334 = 1.054092553

Reorder the terms:
-0.3333333334 + x = 1.054092553

Solving
-0.3333333334 + x = 1.054092553

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.054092553 + 0.3333333334
x = 1.054092553 + 0.3333333334

Combine like terms: 1.054092553 + 0.3333333334 = 1.3874258864
x = 1.3874258864

Simplifying
x = 1.3874258864

Subproblem 2
x + -0.3333333334 = -1.054092553

Simplifying
x + -0.3333333334 = -1.054092553

Reorder the terms:
-0.3333333334 + x = -1.054092553

Solving
-0.3333333334 + x = -1.054092553

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.054092553 + 0.3333333334
x = -1.054092553 + 0.3333333334

Combine like terms: -1.054092553 + 0.3333333334 = -0.7207592196
x = -0.7207592196

Simplifying
x = -0.7207592196

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3874258864, -0.7207592196}
Solution
x = {1.3874258864, -0.7207592196}