Simplifying
5 = 9q + 2q^{2}
Solving
5 = 9q + 2q^{2}
Solving for variable 'q'.
Reorder the terms:
5 + -9q + -2q^{2} = 9q + -9q + 2q^{2} + -2q^{2}
Combine like terms: 9q + -9q = 0
5 + -9q + -2q^{2} = 0 + 2q^{2} + -2q^{2}
5 + -9q + -2q^{2} = 2q^{2} + -2q^{2}
Combine like terms: 2q^{2} + -2q^{2} = 0
5 + -9q + -2q^{2} = 0
Factor a trinomial.
(1 + -2q)(5 + q) = 0
#### Subproblem 1

Set the factor '(1 + -2q)' equal to zero and attempt to solve:
Simplifying
1 + -2q = 0
Solving
1 + -2q = 0
Move all terms containing q to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -2q = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -2q = 0 + -1
-2q = 0 + -1
Combine like terms: 0 + -1 = -1
-2q = -1
Divide each side by '-2'.
q = 0.5
Simplifying
q = 0.5
#### Subproblem 2

Set the factor '(5 + q)' equal to zero and attempt to solve:
Simplifying
5 + q = 0
Solving
5 + q = 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 + q = 0 + -5
Combine like terms: 5 + -5 = 0
0 + q = 0 + -5
q = 0 + -5
Combine like terms: 0 + -5 = -5
q = -5
Simplifying
q = -5#### Solution

q = {0.5, -5}