q^2+q-20=0

Solution for q^2+q-20=0 equation:

Simplifying
q2 + q + -20 = 0

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

Solving
-20 + q + q2 = 0

Solving for variable 'q'.

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

Subproblem 1
Set the factor '(-5 + -1q)' equal to zero and attempt to solve:

Simplifying
-5 + -1q = 0

Solving
-5 + -1q = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1q = 0 + 5
-1q = 0 + 5

Combine like terms: 0 + 5 = 5
-1q = 5

Divide each side by '-1'.
q = -5

Simplifying
q = -5
Subproblem 2
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
Solution
q = {-5, 4}