18x^3-33x^2+18x=0

Solution for 18x^3-33x^2+18x=0 equation:

Simplifying
18x3 + -33x2 + 18x = 0

Reorder the terms:
18x + -33x2 + 18x3 = 0

Solving
18x + -33x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(6 + -11x + 6x2) = 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 '(6 + -11x + 6x2)' equal to zero and attempt to solve:

Simplifying
6 + -11x + 6x2 = 0

Solving
6 + -11x + 6x2 = 0

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

Divide each side by '6'.
1 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.833333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.833333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.833333333x + x2 = 0 + -1
-1.833333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.833333333x + x2 = -1

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = -1 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = -1 + 0.8402777775

Combine like terms: -1 + 0.8402777775 = -0.1597222225
0.8402777775 + -1.833333333x + x2 = -0.1597222225

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = -0.1597222225

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}