(n+5)(n+3)=0

Solution for (n+5)(n+3)=0 equation:

Simplifying
(n + 5)(n + 3) = 0

Reorder the terms:
(5 + n)(n + 3) = 0

Reorder the terms:
(5 + n)(3 + n) = 0

Multiply (5 + n) * (3 + n)
(5(3 + n) + n(3 + n)) = 0
((3 * 5 + n * 5) + n(3 + n)) = 0
((15 + 5n) + n(3 + n)) = 0
(15 + 5n + (3 * n + n * n)) = 0
(15 + 5n + (3n + n2)) = 0

Combine like terms: 5n + 3n = 8n
(15 + 8n + n2) = 0

Solving
15 + 8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + n)(3 + 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 '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {-5, -3}