0=2x^3-6x^2+12x

Solution for 0=2x^3-6x^2+12x equation:

Simplifying
0 = 2x3 + -6x2 + 12x

Reorder the terms:
0 = 12x + -6x2 + 2x3

Solving
0 = 12x + -6x2 + 2x3

Solving for variable 'x'.
Remove the zero:
-12x + 6x2 + -2x3 = 12x + -6x2 + 2x3 + -12x + 6x2 + -2x3

Reorder the terms:
-12x + 6x2 + -2x3 = 12x + -12x + -6x2 + 6x2 + 2x3 + -2x3

Combine like terms: 12x + -12x = 0
-12x + 6x2 + -2x3 = 0 + -6x2 + 6x2 + 2x3 + -2x3
-12x + 6x2 + -2x3 = -6x2 + 6x2 + 2x3 + -2x3

Combine like terms: -6x2 + 6x2 = 0
-12x + 6x2 + -2x3 = 0 + 2x3 + -2x3
-12x + 6x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-12x + 6x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6 + 3x + -1x2) = 0

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

Simplifying
-6 + 3x + -1x2 = 0

Solving
-6 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -3x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -3x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3x + x2 = 0 + -6
-3x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3x + x2 = -6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3x + x2 = -3.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -3.75

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}