2q^2-22q=-60

Solution for 2q^2-22q=-60 equation:

Simplifying
2q2 + -22q = -60

Reorder the terms:
-22q + 2q2 = -60

Solving
-22q + 2q2 = -60

Solving for variable 'q'.

Reorder the terms:
60 + -22q + 2q2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + -22q + 2q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11q + q2) = 0

Factor a trinomial.
2((5 + -1q)(6 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
q = {5, 6}