9r^2-25rs-6s^2=0

Solution for 9r^2-25rs-6s^2=0 equation:

Simplifying
9r2 + -25rs + -6s2 = 0

Reorder the terms:
-25rs + 9r2 + -6s2 = 0

Solving
-25rs + 9r2 + -6s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -3s)(9r + 2s) = 0

Subproblem 1
Set the factor '(r + -3s)' equal to zero and attempt to solve:

Simplifying
r + -3s = 0

Solving
r + -3s = 0

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

Add '3s' to each side of the equation.
r + -3s + 3s = 0 + 3s

Combine like terms: -3s + 3s = 0
r + 0 = 0 + 3s
r = 0 + 3s
Remove the zero:
r = 3s

Simplifying
r = 3s
Subproblem 2
Set the factor '(9r + 2s)' equal to zero and attempt to solve:

Simplifying
9r + 2s = 0

Solving
9r + 2s = 0

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

Add '-2s' to each side of the equation.
9r + 2s + -2s = 0 + -2s

Combine like terms: 2s + -2s = 0
9r + 0 = 0 + -2s
9r = 0 + -2s
Remove the zero:
9r = -2s

Divide each side by '9'.
r = -0.2222222222s

Simplifying
r = -0.2222222222s
Solution
r = {3s, -0.2222222222s}