12n^2+82n+60=0

Solution for 12n^2+82n+60=0 equation:

Simplifying
12n2 + 82n + 60 = 0

Reorder the terms:
60 + 82n + 12n2 = 0

Solving
60 + 82n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + 41n + 6n2) = 0

Factor a trinomial.
2((6 + n)(5 + 6n)) = 0

Ignore the factor 2.
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 '(5 + 6n)' equal to zero and attempt to solve:

Simplifying
5 + 6n = 0

Solving
5 + 6n = 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 + 6n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6n = 0 + -5
6n = 0 + -5

Combine like terms: 0 + -5 = -5
6n = -5

Divide each side by '6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Solution
n = {-6, -0.8333333333}