15r^3+20r^2s-20rs^2=0

Solution for 15r^3+20r^2s-20rs^2=0 equation:

Simplifying
15r3 + 20r2s + -20rs2 = 0

Reorder the terms:
-20rs2 + 20r2s + 15r3 = 0

Solving
-20rs2 + 20r2s + 15r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-4s2 + 4rs + 3r2) = 0

Factor a trinomial.
5r((-2s + -1r)(2s + -3r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-2s + -1r)' equal to zero and attempt to solve:

Simplifying
-2s + -1r = 0

Reorder the terms:
-1r + -2s = 0

Solving
-1r + -2s = 0

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

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

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

Divide each side by '-1'.
r = -2s

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

Simplifying
2s + -3r = 0

Reorder the terms:
-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, -2s, 0.6666666667s}