(n+5)(n+1)=0

Solution for (n+5)(n+1)=0 equation:

Simplifying
(n + 5)(n + 1) = 0

Reorder the terms:
(5 + n)(n + 1) = 0

Reorder the terms:
(5 + n)(1 + n) = 0

Multiply (5 + n) * (1 + n)
(5(1 + n) + n(1 + n)) = 0
((1 * 5 + n * 5) + n(1 + n)) = 0
((5 + 5n) + n(1 + n)) = 0
(5 + 5n + (1 * n + n * n)) = 0
(5 + 5n + (1n + n2)) = 0

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

Solving
5 + 6n + n2 = 0

Solving for variable 'n'.

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

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}