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

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

Simplifying
r2 + rs + -6s2 = 0

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

Solving
rs + r2 + -6s2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {2s, -3s}