0=81-27h+2h^2

Solution for 0=81-27h+2h^2 equation:

Simplifying
0 = 81 + -27h + 2h2

Solving
0 = 81 + -27h + 2h2

Solving for variable 'h'.

Combine like terms: 0 + -81 = -81
-81 + 27h + -2h2 = 81 + -27h + 2h2 + -81 + 27h + -2h2

Reorder the terms:
-81 + 27h + -2h2 = 81 + -81 + -27h + 27h + 2h2 + -2h2

Combine like terms: 81 + -81 = 0
-81 + 27h + -2h2 = 0 + -27h + 27h + 2h2 + -2h2
-81 + 27h + -2h2 = -27h + 27h + 2h2 + -2h2

Combine like terms: -27h + 27h = 0
-81 + 27h + -2h2 = 0 + 2h2 + -2h2
-81 + 27h + -2h2 = 2h2 + -2h2

Combine like terms: 2h2 + -2h2 = 0
-81 + 27h + -2h2 = 0

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

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

Simplifying
-9 + h = 0

Solving
-9 + h = 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 + h = 0 + 9

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

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

Simplifying
h = 9
Subproblem 2
Set the factor '(9 + -2h)' equal to zero and attempt to solve:

Simplifying
9 + -2h = 0

Solving
9 + -2h = 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 + -2h = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2h = 0 + -9
-2h = 0 + -9

Combine like terms: 0 + -9 = -9
-2h = -9

Divide each side by '-2'.
h = 4.5

Simplifying
h = 4.5
Solution
h = {9, 4.5}