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}