n^2+6n+5n=-6

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

Simplifying
n2 + 6n + 5n = -6

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

Combine like terms: 6n + 5n = 11n
11n + n2 = -6

Solving
11n + n2 = -6

Solving for variable 'n'.

Reorder the terms:
6 + 11n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 11n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 11n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + 11n + n2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 11n + n2 = 0 + -6
11n + n2 = 0 + -6

Combine like terms: 0 + -6 = -6
11n + n2 = -6

The n term is 11n.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11n + 30.25 + n2 = -6 + 30.25

Reorder the terms:
30.25 + 11n + n2 = -6 + 30.25

Combine like terms: -6 + 30.25 = 24.25
30.25 + 11n + n2 = 24.25

Factor a perfect square on the left side:
(n + 5.5)(n + 5.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(n + 5.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
n + 5.5 = 4.924428901

Simplifying
n + 5.5 = 4.924428901

Reorder the terms:
5.5 + n = 4.924428901

Solving
5.5 + n = 4.924428901

Solving for variable 'n'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + n = 4.924428901 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + n = 4.924428901 + -5.5
n = 4.924428901 + -5.5

Combine like terms: 4.924428901 + -5.5 = -0.575571099
n = -0.575571099

Simplifying
n = -0.575571099

Subproblem 2
n + 5.5 = -4.924428901

Simplifying
n + 5.5 = -4.924428901

Reorder the terms:
5.5 + n = -4.924428901

Solving
5.5 + n = -4.924428901

Solving for variable 'n'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + n = -4.924428901 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + n = -4.924428901 + -5.5
n = -4.924428901 + -5.5

Combine like terms: -4.924428901 + -5.5 = -10.424428901
n = -10.424428901

Simplifying
n = -10.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.575571099, -10.424428901}