6r^2+5rs-s^2=0

Solution for 6r^2+5rs-s^2=0 equation:

Simplifying
6r2 + 5rs + -1s2 = 0

Reorder the terms:
5rs + 6r2 + -1s2 = 0

Solving
5rs + 6r2 + -1s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6r + -1s)(r + s) = 0

Subproblem 1
Set the factor '(6r + -1s)' equal to zero and attempt to solve:

Simplifying
6r + -1s = 0

Solving
6r + -1s = 0

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

Add 's' to each side of the equation.
6r + -1s + s = 0 + s

Combine like terms: -1s + s = 0
6r + 0 = 0 + s
6r = 0 + s
Remove the zero:
6r = s

Divide each side by '6'.
r = 0.1666666667s

Simplifying
r = 0.1666666667s
Subproblem 2
Set the factor '(r + s)' equal to zero and attempt to solve:

Simplifying
r + s = 0

Solving
r + s = 0

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

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

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

Simplifying
r = -1s
Solution
r = {0.1666666667s, -1s}