6(n+4)(n+2)=0

Solution for 6(n+4)(n+2)=0 equation:

Simplifying
6(n + 4)(n + 2) = 0

Reorder the terms:
6(4 + n)(n + 2) = 0

Reorder the terms:
6(4 + n)(2 + n) = 0

Multiply (4 + n) * (2 + n)
6(4(2 + n) + n(2 + n)) = 0
6((2 * 4 + n * 4) + n(2 + n)) = 0
6((8 + 4n) + n(2 + n)) = 0
6(8 + 4n + (2 * n + n * n)) = 0
6(8 + 4n + (2n + n2)) = 0

Combine like terms: 4n + 2n = 6n
6(8 + 6n + n2) = 0
(8 * 6 + 6n * 6 + n2 * 6) = 0
(48 + 36n + 6n2) = 0

Solving
48 + 36n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + 6n + n2) = 0

Factor a trinomial.
6((4 + n)(2 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
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 = {-4, -2}