3h^2+13h+4=0

Solution for 3h^2+13h+4=0 equation:

Simplifying
3h2 + 13h + 4 = 0

Reorder the terms:
4 + 13h + 3h2 = 0

Solving
4 + 13h + 3h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(4 + h)(1 + 3h) = 0

Subproblem 1
Set the factor '(4 + h)' equal to zero and attempt to solve:

Simplifying
4 + h = 0

Solving
4 + h = 0

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

Add '-4' to each side of the equation.
4 + -4 + h = 0 + -4

Combine like terms: 4 + -4 = 0
0 + h = 0 + -4
h = 0 + -4

Combine like terms: 0 + -4 = -4
h = -4

Simplifying
h = -4
Subproblem 2
Set the factor '(1 + 3h)' equal to zero and attempt to solve:

Simplifying
1 + 3h = 0

Solving
1 + 3h = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3h = 0 + -1
3h = 0 + -1

Combine like terms: 0 + -1 = -1
3h = -1

Divide each side by '3'.
h = -0.3333333333

Simplifying
h = -0.3333333333
Solution
h = {-4, -0.3333333333}