-3q^2+15q-12=0

Solution for -3q^2+15q-12=0 equation:

Simplifying
-3q2 + 15q + -12 = 0

Reorder the terms:
-12 + 15q + -3q2 = 0

Solving
-12 + 15q + -3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 5q + -1q2) = 0

Factor a trinomial.
3((-4 + q)(1 + -1q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + q)' equal to zero and attempt to solve:

Simplifying
-4 + q = 0

Solving
-4 + q = 0

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

Add '4' to each side of the equation.
-4 + 4 + q = 0 + 4

Combine like terms: -4 + 4 = 0
0 + q = 0 + 4
q = 0 + 4

Combine like terms: 0 + 4 = 4
q = 4

Simplifying
q = 4
Subproblem 2
Set the factor '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Solution
q = {4, 1}