6h^2+82h+120=0

Solution for 6h^2+82h+120=0 equation:

Simplifying
6h2 + 82h + 120 = 0

Reorder the terms:
120 + 82h + 6h2 = 0

Solving
120 + 82h + 6h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + 41h + 3h2) = 0

Factor a trinomial.
2((12 + h)(5 + 3h)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + h)' equal to zero and attempt to solve:

Simplifying
12 + h = 0

Solving
12 + h = 0

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

Add '-12' to each side of the equation.
12 + -12 + h = 0 + -12

Combine like terms: 12 + -12 = 0
0 + h = 0 + -12
h = 0 + -12

Combine like terms: 0 + -12 = -12
h = -12

Simplifying
h = -12
Subproblem 2
Set the factor '(5 + 3h)' equal to zero and attempt to solve:

Simplifying
5 + 3h = 0

Solving
5 + 3h = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3h = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3h = 0 + -5
3h = 0 + -5

Combine like terms: 0 + -5 = -5
3h = -5

Divide each side by '3'.
h = -1.666666667

Simplifying
h = -1.666666667
Solution
h = {-12, -1.666666667}