5h^2=-3h+2

Solution for 5h^2=-3h+2 equation:

Simplifying
5h2 = -3h + 2

Reorder the terms:
5h2 = 2 + -3h

Solving
5h2 = 2 + -3h

Solving for variable 'h'.

Reorder the terms:
-2 + 3h + 5h2 = 2 + -3h + -2 + 3h

Reorder the terms:
-2 + 3h + 5h2 = 2 + -2 + -3h + 3h

Combine like terms: 2 + -2 = 0
-2 + 3h + 5h2 = 0 + -3h + 3h
-2 + 3h + 5h2 = -3h + 3h

Combine like terms: -3h + 3h = 0
-2 + 3h + 5h2 = 0

Factor a trinomial.
(-1 + -1h)(2 + -5h) = 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 '(2 + -5h)' equal to zero and attempt to solve:

Simplifying
2 + -5h = 0

Solving
2 + -5h = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5h = 0 + -2
-5h = 0 + -2

Combine like terms: 0 + -2 = -2
-5h = -2

Divide each side by '-5'.
h = 0.4

Simplifying
h = 0.4
Solution
h = {-1, 0.4}