2x^3+18x=12x^2

Solution for 2x^3+18x=12x^2 equation:

Simplifying
2x3 + 18x = 12x2

Reorder the terms:
18x + 2x3 = 12x2

Solving
18x + 2x3 = 12x2

Solving for variable 'x'.

Reorder the terms:
18x + -12x2 + 2x3 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
18x + -12x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -6x + x2) = 0

Factor a trinomial.
2x((3 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
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 '(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, 3, 3}