6n^2-240=-18n

Solution for 6n^2-240=-18n equation:

Simplifying
6n2 + -240 = -18n

Reorder the terms:
-240 + 6n2 = -18n

Solving
-240 + 6n2 = -18n

Solving for variable 'n'.

Reorder the terms:
-240 + 18n + 6n2 = -18n + 18n

Combine like terms: -18n + 18n = 0
-240 + 18n + 6n2 = 0

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

Factor a trinomial.
6((-8 + -1n)(5 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 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 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-8, 5}