(n+3)(n+8)=0

Solution for (n+3)(n+8)=0 equation:

Simplifying
(n + 3)(n + 8) = 0

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

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

Multiply (3 + n) * (8 + n)
(3(8 + n) + n(8 + n)) = 0
((8 * 3 + n * 3) + n(8 + n)) = 0
((24 + 3n) + n(8 + n)) = 0
(24 + 3n + (8 * n + n * n)) = 0
(24 + 3n + (8n + n2)) = 0

Combine like terms: 3n + 8n = 11n
(24 + 11n + n2) = 0

Solving
24 + 11n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(3 + 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 '(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 = {-8, -3}