4q^2+32q+60=0

Solution for 4q^2+32q+60=0 equation:

Simplifying
4q2 + 32q + 60 = 0

Reorder the terms:
60 + 32q + 4q2 = 0

Solving
60 + 32q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 8q + q2) = 0

Factor a trinomial.
4((5 + q)(3 + q)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + q)' equal to zero and attempt to solve:

Simplifying
5 + q = 0

Solving
5 + q = 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 + q = 0 + -5

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

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

Simplifying
q = -5
Subproblem 2
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 0

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

Add '-3' to each side of the equation.
3 + -3 + q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + q = 0 + -3
q = 0 + -3

Combine like terms: 0 + -3 = -3
q = -3

Simplifying
q = -3
Solution
q = {-5, -3}