n(2n+6)=108

Solution for n(2n+6)=108 equation:

Simplifying
n(2n + 6) = 108

Reorder the terms:
n(6 + 2n) = 108
(6 * n + 2n * n) = 108
(6n + 2n2) = 108

Solving
6n + 2n2 = 108

Solving for variable 'n'.

Reorder the terms:
-108 + 6n + 2n2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 3n + n2) = 0

Factor a trinomial.
2((-9 + -1n)(6 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-9, 6}