6x^3-6x^2+9x=0

Solution for 6x^3-6x^2+9x=0 equation:

Simplifying
6x3 + -6x2 + 9x = 0

Reorder the terms:
9x + -6x2 + 6x3 = 0

Solving
9x + -6x2 + 6x3 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + -2x + 2x2 = 0

Solving
3 + -2x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1x + x2 = 0 + -1.5
-1x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1x + x2 = -1.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -1x + x2 = -1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.25

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}