n(3n+18)=120

Solution for n(3n+18)=120 equation:

Simplifying
n(3n + 18) = 120

Reorder the terms:
n(18 + 3n) = 120
(18 * n + 3n * n) = 120
(18n + 3n2) = 120

Solving
18n + 3n2 = 120

Solving for variable 'n'.

Reorder the terms:
-120 + 18n + 3n2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 18n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + 6n + n2) = 0

Factor a trinomial.
3((-10 + -1n)(4 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-10, 4}