n^2+9n=-20

Solution for n^2+9n=-20 equation:

Simplifying
n2 + 9n = -20

Reorder the terms:
9n + n2 = -20

Solving
9n + n2 = -20

Solving for variable 'n'.

Reorder the terms:
20 + 9n + n2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 9n + n2 = 0

Factor a trinomial.
(5 + n)(4 + n) = 0

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

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-5, -4}