x^3+3x^2=18x

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

Simplifying
x3 + 3x2 = 18x

Reorder the terms:
3x2 + x3 = 18x

Solving
3x2 + x3 = 18x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 3x + x2) = 0

Factor a trinomial.
x((-6 + -1x)(3 + -1x)) = 0

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)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 3
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
Solution
x = {0, -6, 3}