3q^3+3q^2=90q

Solution for 3q^3+3q^2=90q equation:

Simplifying
3q3 + 3q2 = 90q

Reorder the terms:
3q2 + 3q3 = 90q

Solving
3q2 + 3q3 = 90q

Solving for variable 'q'.

Reorder the terms:
-90q + 3q2 + 3q3 = 90q + -90q

Combine like terms: 90q + -90q = 0
-90q + 3q2 + 3q3 = 0

Factor out the Greatest Common Factor (GCF), '3q'.
3q(-30 + q + q2) = 0

Factor a trinomial.
3q((-6 + -1q)(5 + -1q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(-6 + -1q)' equal to zero and attempt to solve:

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 0

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

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

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

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

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

Simplifying
q = -6
Subproblem 3
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {0, -6, 5}