n^2+8=-6n

Solution for n^2+8=-6n equation:

Simplifying
n2 + 8 = -6n

Reorder the terms:
8 + n2 = -6n

Solving
8 + n2 = -6n

Solving for variable 'n'.

Reorder the terms:
8 + 6n + n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
8 + 6n + n2 = 0

Factor a trinomial.
(4 + n)(2 + 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 '(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 = {-4, -2}