-2q^2+4q+48=0

Solution for -2q^2+4q+48=0 equation:

Simplifying
-2q2 + 4q + 48 = 0

Reorder the terms:
48 + 4q + -2q2 = 0

Solving
48 + 4q + -2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 2q + -1q2) = 0

Factor a trinomial.
2((6 + -1q)(4 + q)) = 0

Ignore the factor 2.
Subproblem 1
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 2
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
Solution
q = {6, -4}