q^2-q=20

Solution for q^2-q=20 equation:

Simplifying
q2 + -1q = 20

Reorder the terms:
-1q + q2 = 20

Solving
-1q + q2 = 20

Solving for variable 'q'.

Reorder the terms:
-20 + -1q + q2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -1q + q2 = 0

Factor a trinomial.
(-4 + -1q)(5 + -1q) = 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 '(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
Solution
q = {-4, 5}