n^2+5=-6n

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

Simplifying
n2 + 5 = -6n

Reorder the terms:
5 + n2 = -6n

Solving
5 + n2 = -6n

Solving for variable 'n'.

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

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

Factor a trinomial.
(5 + n)(1 + 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 '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Solution
n = {-5, -1}