3x^3+3x^2=18x

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

Simplifying
3x3 + 3x2 = 18x

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

Solving
3x2 + 3x3 = 18x

Solving for variable 'x'.

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

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

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

Factor a trinomial.
3x((-3 + -1x)(2 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -3, 2}