s^2+5sh-36h^2=0

Solution for s^2+5sh-36h^2=0 equation:

Simplifying
s2 + 5sh + -36h2 = 0

Reorder the terms:
5hs + -36h2 + s2 = 0

Solving
5hs + -36h2 + s2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-9h + -1s)(4h + -1s) = 0

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

Simplifying
-9h + -1s = 0

Solving
-9h + -1s = 0

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

Add 's' to each side of the equation.
-9h + -1s + s = 0 + s

Combine like terms: -1s + s = 0
-9h + 0 = 0 + s
-9h = 0 + s
Remove the zero:
-9h = s

Divide each side by '-9'.
h = -0.1111111111s

Simplifying
h = -0.1111111111s
Subproblem 2
Set the factor '(4h + -1s)' equal to zero and attempt to solve:

Simplifying
4h + -1s = 0

Solving
4h + -1s = 0

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

Add 's' to each side of the equation.
4h + -1s + s = 0 + s

Combine like terms: -1s + s = 0
4h + 0 = 0 + s
4h = 0 + s
Remove the zero:
4h = s

Divide each side by '4'.
h = 0.25s

Simplifying
h = 0.25s
Solution
h = {-0.1111111111s, 0.25s}