Simplifying
5 = 9q + 2q2

Solving
5 = 9q + 2q2

Solving for variable 'q'.

Reorder the terms:
5 + -9q + -2q2 = 9q + -9q + 2q2 + -2q2

Combine like terms: 9q + -9q = 0
5 + -9q + -2q2 = 0 + 2q2 + -2q2
5 + -9q + -2q2 = 2q2 + -2q2

Combine like terms: 2q2 + -2q2 = 0
5 + -9q + -2q2 = 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}