-4Q^2+52Q-120=0

Solution for -4Q^2+52Q-120=0 equation:

Simplifying
-4Q2 + 52Q + -120 = 0

Reorder the terms:
-120 + 52Q + -4Q2 = 0

Solving
-120 + 52Q + -4Q2 = 0

Solving for variable 'Q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 13Q + -1Q2) = 0

Factor a trinomial.
4((-10 + Q)(3 + -1Q)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-10 + Q)' equal to zero and attempt to solve:

Simplifying
-10 + Q = 0

Solving
-10 + Q = 0

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

Add '10' to each side of the equation.
-10 + 10 + Q = 0 + 10

Combine like terms: -10 + 10 = 0
0 + Q = 0 + 10
Q = 0 + 10

Combine like terms: 0 + 10 = 10
Q = 10

Simplifying
Q = 10
Subproblem 2
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
Solution
Q = {10, 3}