12x^2=x^3+27x

Solution for 12x^2=x^3+27x equation:

Simplifying
12x2 = x3 + 27x

Reorder the terms:
12x2 = 27x + x3

Solving
12x2 = 27x + x3

Solving for variable 'x'.

Reorder the terms:
-27x + 12x2 + -1x3 = 27x + x3 + -27x + -1x3

Reorder the terms:
-27x + 12x2 + -1x3 = 27x + -27x + x3 + -1x3

Combine like terms: 27x + -27x = 0
-27x + 12x2 + -1x3 = 0 + x3 + -1x3
-27x + 12x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-27x + 12x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + 12x + -1x2) = 0

Factor a trinomial.
x((-9 + x)(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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
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, 9, 3}