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Simplifying
20q2 + -13q + 2 = 0

Reorder the terms:
2 + -13q + 20q2 = 0

Solving
2 + -13q + 20q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -4q)(2 + -5q) = 0

Subproblem 1

Set the factor '(1 + -4q)' equal to zero and attempt to solve: Simplifying 1 + -4q = 0 Solving 1 + -4q = 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 + -4q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4q = 0 + -1 -4q = 0 + -1 Combine like terms: 0 + -1 = -1 -4q = -1 Divide each side by '-4'. q = 0.25 Simplifying q = 0.25

Subproblem 2

Set the factor '(2 + -5q)' equal to zero and attempt to solve: Simplifying 2 + -5q = 0 Solving 2 + -5q = 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 + -5q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5q = 0 + -2 -5q = 0 + -2 Combine like terms: 0 + -2 = -2 -5q = -2 Divide each side by '-5'. q = 0.4 Simplifying q = 0.4

Solution

q = {0.25, 0.4}
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