32=20-5q+2q^2

Solution for 32=20-5q+2q^2 equation:

Simplifying
32 = 20 + -5q + 2q2

Solving
32 = 20 + -5q + 2q2

Solving for variable 'q'.

Combine like terms: 32 + -20 = 12
12 + 5q + -2q2 = 20 + -5q + 2q2 + -20 + 5q + -2q2

Reorder the terms:
12 + 5q + -2q2 = 20 + -20 + -5q + 5q + 2q2 + -2q2

Combine like terms: 20 + -20 = 0
12 + 5q + -2q2 = 0 + -5q + 5q + 2q2 + -2q2
12 + 5q + -2q2 = -5q + 5q + 2q2 + -2q2

Combine like terms: -5q + 5q = 0
12 + 5q + -2q2 = 0 + 2q2 + -2q2
12 + 5q + -2q2 = 2q2 + -2q2

Combine like terms: 2q2 + -2q2 = 0
12 + 5q + -2q2 = 0

Factor a trinomial.
(4 + -1q)(3 + 2q) = 0

Subproblem 1
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Subproblem 2
Set the factor '(3 + 2q)' equal to zero and attempt to solve:

Simplifying
3 + 2q = 0

Solving
3 + 2q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2q = 0 + -3
2q = 0 + -3

Combine like terms: 0 + -3 = -3
2q = -3

Divide each side by '2'.
q = -1.5

Simplifying
q = -1.5
Solution
q = {4, -1.5}