q^2-8q-20=0

Solution for q^2-8q-20=0 equation:

Simplifying
q2 + -8q + -20 = 0

Reorder the terms:
-20 + -8q + q2 = 0

Solving
-20 + -8q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-2 + -1q)(10 + -1q) = 0

Subproblem 1
Set the factor '(-2 + -1q)' equal to zero and attempt to solve:

Simplifying
-2 + -1q = 0

Solving
-2 + -1q = 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 + -1q = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1q = 0 + 2
-1q = 0 + 2

Combine like terms: 0 + 2 = 2
-1q = 2

Divide each side by '-1'.
q = -2

Simplifying
q = -2
Subproblem 2
Set the factor '(10 + -1q)' equal to zero and attempt to solve:

Simplifying
10 + -1q = 0

Solving
10 + -1q = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1q = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1q = 0 + -10
-1q = 0 + -10

Combine like terms: 0 + -10 = -10
-1q = -10

Divide each side by '-1'.
q = 10

Simplifying
q = 10
Solution
q = {-2, 10}