n^2+15n=-56

Solution for n^2+15n=-56 equation:

Simplifying
n2 + 15n = -56

Reorder the terms:
15n + n2 = -56

Solving
15n + n2 = -56

Solving for variable 'n'.

Reorder the terms:
56 + 15n + n2 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + 15n + n2 = 0

Factor a trinomial.
(8 + n)(7 + n) = 0

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
Solution
n = {-8, -7}