6n^2+72n+192=

Solution for 6n^2+72n+192= equation:

Simplifying
6n2 + 72n + 192 = 0

Reorder the terms:
192 + 72n + 6n2 = 0

Solving
192 + 72n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(32 + 12n + n2) = 0

Factor a trinomial.
6((8 + n)(4 + n)) = 0

Ignore the factor 6.
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 '(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
Solution
n = {-8, -4}