3h^2+17h+10=0

Solution for 3h^2+17h+10=0 equation:

Simplifying
3h2 + 17h + 10 = 0

Reorder the terms:
10 + 17h + 3h2 = 0

Solving
10 + 17h + 3h2 = 0

Solving for variable 'h'.

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

Subproblem 1
Set the factor '(5 + h)' equal to zero and attempt to solve:

Simplifying
5 + h = 0

Solving
5 + h = 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 + h = 0 + -5

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

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

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

Simplifying
2 + 3h = 0

Solving
2 + 3h = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3h = 0 + -2
3h = 0 + -2

Combine like terms: 0 + -2 = -2
3h = -2

Divide each side by '3'.
h = -0.6666666667

Simplifying
h = -0.6666666667
Solution
h = {-5, -0.6666666667}