(n+2)(n+6)=0

Solution for (n+2)(n+6)=0 equation:

Simplifying
(n + 2)(n + 6) = 0

Reorder the terms:
(2 + n)(n + 6) = 0

Reorder the terms:
(2 + n)(6 + n) = 0

Multiply (2 + n) * (6 + n)
(2(6 + n) + n(6 + n)) = 0
((6 * 2 + n * 2) + n(6 + n)) = 0
((12 + 2n) + n(6 + n)) = 0
(12 + 2n + (6 * n + n * n)) = 0
(12 + 2n + (6n + n2)) = 0

Combine like terms: 2n + 6n = 8n
(12 + 8n + n2) = 0

Solving
12 + 8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + n)(2 + n) = 0

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
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 = {-6, -2}