-10r^2-11sr+6s^2=0

Solution for -10r^2-11sr+6s^2=0 equation:

Simplifying
-10r2 + -11sr + 6s2 = 0

Reorder the terms:
-11rs + -10r2 + 6s2 = 0

Solving
-11rs + -10r2 + 6s2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-2r + -3s)' equal to zero and attempt to solve:

Simplifying
-2r + -3s = 0

Solving
-2r + -3s = 0

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

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

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

Divide each side by '-2'.
r = -1.5s

Simplifying
r = -1.5s
Subproblem 2
Set the factor '(5r + -2s)' equal to zero and attempt to solve:

Simplifying
5r + -2s = 0

Solving
5r + -2s = 0

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

Add '2s' to each side of the equation.
5r + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
5r + 0 = 0 + 2s
5r = 0 + 2s
Remove the zero:
5r = 2s

Divide each side by '5'.
r = 0.4s

Simplifying
r = 0.4s
Solution
r = {-1.5s, 0.4s}