15n^2+110n=-120

Solution for 15n^2+110n=-120 equation:

Simplifying
15n2 + 110n = -120

Reorder the terms:
110n + 15n2 = -120

Solving
110n + 15n2 = -120

Solving for variable 'n'.

Reorder the terms:
120 + 110n + 15n2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + 110n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + 22n + 3n2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

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

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

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

Simplifying
n = -6
Subproblem 2
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
Solution
n = {-6, -1.333333333}