6r^2+rs-2s^2=0

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

Simplifying
6r2 + rs + -2s2 = 0

Reorder the terms:
rs + 6r2 + -2s2 = 0

Solving
rs + 6r2 + -2s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2r + -1s)(3r + 2s) = 0

Subproblem 1
Set the factor '(2r + -1s)' equal to zero and attempt to solve:

Simplifying
2r + -1s = 0

Solving
2r + -1s = 0

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

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

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

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

Simplifying
r = 0.5s
Subproblem 2
Set the factor '(3r + 2s)' equal to zero and attempt to solve:

Simplifying
3r + 2s = 0

Solving
3r + 2s = 0

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

Add '-2s' to each side of the equation.
3r + 2s + -2s = 0 + -2s

Combine like terms: 2s + -2s = 0
3r + 0 = 0 + -2s
3r = 0 + -2s
Remove the zero:
3r = -2s

Divide each side by '3'.
r = -0.6666666667s

Simplifying
r = -0.6666666667s
Solution
r = {0.5s, -0.6666666667s}