8h^2+22h+9=0

Solution for 8h^2+22h+9=0 equation:

Simplifying
8h2 + 22h + 9 = 0

Reorder the terms:
9 + 22h + 8h2 = 0

Solving
9 + 22h + 8h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(9 + 4h)(1 + 2h) = 0

Subproblem 1
Set the factor '(9 + 4h)' equal to zero and attempt to solve:

Simplifying
9 + 4h = 0

Solving
9 + 4h = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4h = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4h = 0 + -9
4h = 0 + -9

Combine like terms: 0 + -9 = -9
4h = -9

Divide each side by '4'.
h = -2.25

Simplifying
h = -2.25
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 = {-2.25, -0.5}