n^2+10n+11=-5

Solution for n^2+10n+11=-5 equation:

Simplifying
n2 + 10n + 11 = -5

Reorder the terms:
11 + 10n + n2 = -5

Solving
11 + 10n + n2 = -5

Solving for variable 'n'.

Reorder the terms:
11 + 5 + 10n + n2 = -5 + 5

Combine like terms: 11 + 5 = 16
16 + 10n + n2 = -5 + 5

Combine like terms: -5 + 5 = 0
16 + 10n + n2 = 0

Factor a trinomial.
(8 + n)(2 + 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 '(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 = {-8, -2}