5n=-6-n^2

Solution for 5n=-6-n^2 equation:

Simplifying
5n = -6 + -1n2

Solving
5n = -6 + -1n2

Solving for variable 'n'.

Reorder the terms:
6 + 5n + n2 = -6 + -1n2 + 6 + n2

Reorder the terms:
6 + 5n + n2 = -6 + 6 + -1n2 + n2

Combine like terms: -6 + 6 = 0
6 + 5n + n2 = 0 + -1n2 + n2
6 + 5n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
6 + 5n + n2 = 0

Factor a trinomial.
(3 + n)(2 + n) = 0

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
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 = {-3, -2}