20=8-4q+q^2

Solution for 20=8-4q+q^2 equation:

Simplifying
20 = 8 + -4q + q2

Solving
20 = 8 + -4q + q2

Solving for variable 'q'.

Combine like terms: 20 + -8 = 12
12 + 4q + -1q2 = 8 + -4q + q2 + -8 + 4q + -1q2

Reorder the terms:
12 + 4q + -1q2 = 8 + -8 + -4q + 4q + q2 + -1q2

Combine like terms: 8 + -8 = 0
12 + 4q + -1q2 = 0 + -4q + 4q + q2 + -1q2
12 + 4q + -1q2 = -4q + 4q + q2 + -1q2

Combine like terms: -4q + 4q = 0
12 + 4q + -1q2 = 0 + q2 + -1q2
12 + 4q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
12 + 4q + -1q2 = 0

Factor a trinomial.
(6 + -1q)(2 + q) = 0

Subproblem 1
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Subproblem 2
Set the factor '(2 + q)' equal to zero and attempt to solve:

Simplifying
2 + q = 0

Solving
2 + q = 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 + q = 0 + -2

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

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

Simplifying
q = -2
Solution
q = {6, -2}