r^2+7rh-18h^2=0

Solution for r^2+7rh-18h^2=0 equation:

Simplifying
r2 + 7rh + -18h2 = 0

Reorder the terms:
7hr + -18h2 + r2 = 0

Solving
7hr + -18h2 + r2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-9h + -1r)(2h + -1r) = 0

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

Simplifying
-9h + -1r = 0

Solving
-9h + -1r = 0

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

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

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

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

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

Simplifying
2h + -1r = 0

Solving
2h + -1r = 0

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

Add 'r' to each side of the equation.
2h + -1r + r = 0 + r

Combine like terms: -1r + r = 0
2h + 0 = 0 + r
2h = 0 + r
Remove the zero:
2h = r

Divide each side by '2'.
h = 0.5r

Simplifying
h = 0.5r
Solution
h = {-0.1111111111r, 0.5r}