Simplifying
20q^{2} + -13q + 2 = 0
Reorder the terms:
2 + -13q + 20q^{2} = 0
Solving
2 + -13q + 20q^{2} = 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}