4h^2+8h+3=0

Solution for 4h^2+8h+3=0 equation:

Simplifying
4h2 + 8h + 3 = 0

Reorder the terms:
3 + 8h + 4h2 = 0

Solving
3 + 8h + 4h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(3 + 2h)(1 + 2h) = 0

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

Simplifying
3 + 2h = 0

Solving
3 + 2h = 0

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

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

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

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

Divide each side by '2'.
h = -1.5

Simplifying
h = -1.5
Subproblem 2
Set the factor '(1 + 2h)' equal to zero and attempt to solve:

Simplifying
1 + 2h = 0

Solving
1 + 2h = 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 + 2h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2h = 0 + -1
2h = 0 + -1

Combine like terms: 0 + -1 = -1
2h = -1

Divide each side by '2'.
h = -0.5

Simplifying
h = -0.5
Solution
h = {-1.5, -0.5}