n^2+4=-5n

Solution for n^2+4=-5n equation:

Simplifying
n2 + 4 = -5n

Reorder the terms:
4 + n2 = -5n

Solving
4 + n2 = -5n

Solving for variable 'n'.

Reorder the terms:
4 + 5n + n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
4 + 5n + n2 = 0

Factor a trinomial.
(4 + n)(1 + n) = 0

Subproblem 1
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
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 = {-4, -1}