(n+2)(n+12)=0

Solution for (n+2)(n+12)=0 equation:

Simplifying
(n + 2)(n + 12) = 0

Reorder the terms:
(2 + n)(n + 12) = 0

Reorder the terms:
(2 + n)(12 + n) = 0

Multiply (2 + n) * (12 + n)
(2(12 + n) + n(12 + n)) = 0
((12 * 2 + n * 2) + n(12 + n)) = 0
((24 + 2n) + n(12 + n)) = 0
(24 + 2n + (12 * n + n * n)) = 0
(24 + 2n + (12n + n2)) = 0

Combine like terms: 2n + 12n = 14n
(24 + 14n + n2) = 0

Solving
24 + 14n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
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 = {-12, -2}