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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}
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