0=n^2+6n+5

Solution for 0=n^2+6n+5 equation:

Simplifying
0 = n2 + 6n + 5

Reorder the terms:
0 = 5 + 6n + n2

Solving
0 = 5 + 6n + n2

Solving for variable 'n'.

Combine like terms: 0 + -5 = -5
-5 + -6n + -1n2 = 5 + 6n + n2 + -5 + -6n + -1n2

Reorder the terms:
-5 + -6n + -1n2 = 5 + -5 + 6n + -6n + n2 + -1n2

Combine like terms: 5 + -5 = 0
-5 + -6n + -1n2 = 0 + 6n + -6n + n2 + -1n2
-5 + -6n + -1n2 = 6n + -6n + n2 + -1n2

Combine like terms: 6n + -6n = 0
-5 + -6n + -1n2 = 0 + n2 + -1n2
-5 + -6n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-5 + -6n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6n + n2) = 0

Factor a trinomial.
-1((5 + n)(1 + n)) = 0

Ignore the factor -1.
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}