18n^2-114n=-120

Solution for 18n^2-114n=-120 equation:

Simplifying
18n2 + -114n = -120

Reorder the terms:
-114n + 18n2 = -120

Solving
-114n + 18n2 = -120

Solving for variable 'n'.

Reorder the terms:
120 + -114n + 18n2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + -114n + 18n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + -19n + 3n2) = 0

Factor a trinomial.
6((4 + -3n)(5 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
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 = {1.333333333, 5}