2h^2-h-3=0

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

Simplifying
2h2 + -1h + -3 = 0

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

Solving
-3 + -1h + 2h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-1 + -1h)(3 + -2h) = 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 '(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
Solution
h = {-1, 1.5}