3r^2+rs-10s^2=0

Solution for 3r^2+rs-10s^2=0 equation:

Simplifying
3r2 + rs + -10s2 = 0

Reorder the terms:
rs + 3r2 + -10s2 = 0

Solving
rs + 3r2 + -10s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + -5s)(r + 2s) = 0

Subproblem 1
Set the factor '(3r + -5s)' equal to zero and attempt to solve:

Simplifying
3r + -5s = 0

Solving
3r + -5s = 0

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

Add '5s' to each side of the equation.
3r + -5s + 5s = 0 + 5s

Combine like terms: -5s + 5s = 0
3r + 0 = 0 + 5s
3r = 0 + 5s
Remove the zero:
3r = 5s

Divide each side by '3'.
r = 1.666666667s

Simplifying
r = 1.666666667s
Subproblem 2
Set the factor '(r + 2s)' equal to zero and attempt to solve:

Simplifying
r + 2s = 0

Solving
r + 2s = 0

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

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

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

Simplifying
r = -2s
Solution
r = {1.666666667s, -2s}