(n+5)(n+8)=0

Solution for (n+5)(n+8)=0 equation:

Simplifying
(n + 5)(n + 8) = 0

Reorder the terms:
(5 + n)(n + 8) = 0

Reorder the terms:
(5 + n)(8 + n) = 0

Multiply (5 + n) * (8 + n)
(5(8 + n) + n(8 + n)) = 0
((8 * 5 + n * 5) + n(8 + n)) = 0
((40 + 5n) + n(8 + n)) = 0
(40 + 5n + (8 * n + n * n)) = 0
(40 + 5n + (8n + n2)) = 0

Combine like terms: 5n + 8n = 13n
(40 + 13n + n2) = 0

Solving
40 + 13n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(5 + 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 '(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
Solution
n = {-8, -5}