15r^2-6rs-20rs-8s^2=0

Solution for 15r^2-6rs-20rs-8s^2=0 equation:

Simplifying
15r2 + -6rs + -20rs + -8s2 = 0

Reorder the terms:
-6rs + -20rs + 15r2 + -8s2 = 0

Combine like terms: -6rs + -20rs = -26rs
-26rs + 15r2 + -8s2 = 0

Solving
-26rs + 15r2 + -8s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -2s)(15r + 4s) = 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 '(15r + 4s)' equal to zero and attempt to solve:

Simplifying
15r + 4s = 0

Solving
15r + 4s = 0

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

Add '-4s' to each side of the equation.
15r + 4s + -4s = 0 + -4s

Combine like terms: 4s + -4s = 0
15r + 0 = 0 + -4s
15r = 0 + -4s
Remove the zero:
15r = -4s

Divide each side by '15'.
r = -0.2666666667s

Simplifying
r = -0.2666666667s
Solution
r = {2s, -0.2666666667s}