-3h^2+2h+1=0

Solution for -3h^2+2h+1=0 equation:

Simplifying
-3h2 + 2h + 1 = 0

Reorder the terms:
1 + 2h + -3h2 = 0

Solving
1 + 2h + -3h2 = 0

Solving for variable 'h'.

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

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

Simplifying
1 + -1h = 0

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

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

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

Divide each side by '-1'.
h = 1

Simplifying
h = 1
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 = {1, -0.3333333333}