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

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

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

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

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

Multiply (2 + n) * (8 + n)
(2(8 + n) + n(8 + n)) = 0
((8 * 2 + n * 2) + n(8 + n)) = 0
((16 + 2n) + n(8 + n)) = 0
(16 + 2n + (8 * n + n * n)) = 0
(16 + 2n + (8n + n2)) = 0

Combine like terms: 2n + 8n = 10n
(16 + 10n + n2) = 0

Solving
16 + 10n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(2 + 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 '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-8, -2}