8h^2+12h+4=0

Solution for 8h^2+12h+4=0 equation:

Simplifying
8h2 + 12h + 4 = 0

Reorder the terms:
4 + 12h + 8h2 = 0

Solving
4 + 12h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 3h + 2h2) = 0

Factor a trinomial.
4((1 + h)(1 + 2h)) = 0

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

Simplifying
1 + h = 0

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

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

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

Simplifying
h = -1
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, -0.5}