(2n+8)(n+5)=0

Solution for (2n+8)(n+5)=0 equation:

Simplifying
(2n + 8)(n + 5) = 0

Reorder the terms:
(8 + 2n)(n + 5) = 0

Reorder the terms:
(8 + 2n)(5 + n) = 0

Multiply (8 + 2n) * (5 + n)
(8(5 + n) + 2n * (5 + n)) = 0
((5 * 8 + n * 8) + 2n * (5 + n)) = 0
((40 + 8n) + 2n * (5 + n)) = 0
(40 + 8n + (5 * 2n + n * 2n)) = 0
(40 + 8n + (10n + 2n2)) = 0

Combine like terms: 8n + 10n = 18n
(40 + 18n + 2n2) = 0

Solving
40 + 18n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 9n + n2) = 0

Factor a trinomial.
2((5 + n)(4 + n)) = 0

Ignore the factor 2.
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 '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-5, -4}