5h^2+2h+5=8

Solution for 5h^2+2h+5=8 equation:

Simplifying
5h2 + 2h + 5 = 8

Reorder the terms:
5 + 2h + 5h2 = 8

Solving
5 + 2h + 5h2 = 8

Solving for variable 'h'.

Reorder the terms:
5 + -8 + 2h + 5h2 = 8 + -8

Combine like terms: 5 + -8 = -3
-3 + 2h + 5h2 = 8 + -8

Combine like terms: 8 + -8 = 0
-3 + 2h + 5h2 = 0

Factor a trinomial.
(-1 + -1h)(3 + -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 '(3 + -5h)' equal to zero and attempt to solve:

Simplifying
3 + -5h = 0

Solving
3 + -5h = 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 + -5h = 0 + -3

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

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

Divide each side by '-5'.
h = 0.6

Simplifying
h = 0.6
Solution
h = {-1, 0.6}