3x^3=3x^2-18x

Solution for 3x^3=3x^2-18x equation:

Simplifying
3x3 = 3x2 + -18x

Reorder the terms:
3x3 = -18x + 3x2

Solving
3x3 = -18x + 3x2

Solving for variable 'x'.

Reorder the terms:
18x + -3x2 + 3x3 = -18x + 3x2 + 18x + -3x2

Reorder the terms:
18x + -3x2 + 3x3 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
18x + -3x2 + 3x3 = 0 + 3x2 + -3x2
18x + -3x2 + 3x3 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18x + -3x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(6 + -1x + x2) = 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 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x + x2 = 0

Solving
6 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -1x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -1x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x + x2 = 0 + -6
-1x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x + x2 = -6

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 = -6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + -1x + x2 = -5.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -5.75

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}