-120+72Q-6Q^2=0

Solution for -120+72Q-6Q^2=0 equation:

Simplifying
-120 + 72Q + -6Q2 = 0

Solving
-120 + 72Q + -6Q2 = 0

Solving for variable 'Q'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + 12Q + -1Q2) = 0

Factor a trinomial.
6((-10 + Q)(2 + -1Q)) = 0

Ignore the factor 6.
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 '(2 + -1Q)' equal to zero and attempt to solve:

Simplifying
2 + -1Q = 0

Solving
2 + -1Q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1Q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1Q = 0 + -2
-1Q = 0 + -2

Combine like terms: 0 + -2 = -2
-1Q = -2

Divide each side by '-1'.
Q = 2

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