N^2+12N=-20

Solution for N^2+12N=-20 equation:

Simplifying
N2 + 12N = -20

Reorder the terms:
12N + N2 = -20

Solving
12N + N2 = -20

Solving for variable 'N'.

Reorder the terms:
20 + 12N + N2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 12N + N2 = 0

Factor a trinomial.
(10 + N)(2 + N) = 0

Subproblem 1
Set the factor '(10 + N)' equal to zero and attempt to solve:

Simplifying
10 + N = 0

Solving
10 + N = 0

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

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

Combine like terms: 10 + -10 = 0
0 + N = 0 + -10
N = 0 + -10

Combine like terms: 0 + -10 = -10
N = -10

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

Simplifying
2 + N = 0

Solving
2 + N = 0

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

Add '-2' to each side of the equation.
2 + -2 + N = 0 + -2

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

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

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