4q^2-8q-60=0

Solution for 4q^2-8q-60=0 equation:

Simplifying
4q2 + -8q + -60 = 0

Reorder the terms:
-60 + -8q + 4q2 = 0

Solving
-60 + -8q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2q + q2) = 0

Factor a trinomial.
4((-3 + -1q)(5 + -1q)) = 0

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

Simplifying
-3 + -1q = 0

Solving
-3 + -1q = 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 + -1q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1q = 0 + 3
-1q = 0 + 3

Combine like terms: 0 + 3 = 3
-1q = 3

Divide each side by '-1'.
q = -3

Simplifying
q = -3
Subproblem 2
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 = {-3, 5}