2x(6x^2-8x+6)=0

Solution for 2x(6x^2-8x+6)=0 equation:

Simplifying
2x(6x2 + -8x + 6) = 0

Reorder the terms:
2x(6 + -8x + 6x2) = 0
(6 * 2x + -8x * 2x + 6x2 * 2x) = 0
(12x + -16x2 + 12x3) = 0

Solving
12x + -16x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + -4x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x + 3x2 = 0

Solving
3 + -4x + 3x2 = 0

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

Divide each side by '3'.
1 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.333333333x + x2 = 0 + -1
-1.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.333333333x + x2 = -1

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 = -1 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1 + 0.4444444442

Combine like terms: -1 + 0.4444444442 = -0.5555555558
0.4444444442 + -1.333333333x + x2 = -0.5555555558

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -0.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}