3h^2+5h-138=0

Solution for 3h^2+5h-138=0 equation:

Simplifying
3h2 + 5h + -138 = 0

Reorder the terms:
-138 + 5h + 3h2 = 0

Solving
-138 + 5h + 3h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-23 + -3h)(6 + -1h) = 0

Subproblem 1
Set the factor '(-23 + -3h)' equal to zero and attempt to solve:

Simplifying
-23 + -3h = 0

Solving
-23 + -3h = 0

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

Add '23' to each side of the equation.
-23 + 23 + -3h = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -3h = 0 + 23
-3h = 0 + 23

Combine like terms: 0 + 23 = 23
-3h = 23

Divide each side by '-3'.
h = -7.666666667

Simplifying
h = -7.666666667
Subproblem 2
Set the factor '(6 + -1h)' equal to zero and attempt to solve:

Simplifying
6 + -1h = 0

Solving
6 + -1h = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1h = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1h = 0 + -6
-1h = 0 + -6

Combine like terms: 0 + -6 = -6
-1h = -6

Divide each side by '-1'.
h = 6

Simplifying
h = 6
Solution
h = {-7.666666667, 6}