3n^2+2n-120=0

Solution for 3n^2+2n-120=0 equation:

Simplifying
3n2 + 2n + -120 = 0

Reorder the terms:
-120 + 2n + 3n2 = 0

Solving
-120 + 2n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-20 + -3n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-20 + -3n)' equal to zero and attempt to solve:

Simplifying
-20 + -3n = 0

Solving
-20 + -3n = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3n = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3n = 0 + 20
-3n = 0 + 20

Combine like terms: 0 + 20 = 20
-3n = 20

Divide each side by '-3'.
n = -6.666666667

Simplifying
n = -6.666666667
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 = {-6.666666667, 6}