24r^2s^7-6r^2s^3+72r^3s^4=0

Solution for 24r^2s^7-6r^2s^3+72r^3s^4=0 equation:

Simplifying
24r2s7 + -6r2s3 + 72r3s4 = 0

Reorder the terms:
-6r2s3 + 24r2s7 + 72r3s4 = 0

Solving
-6r2s3 + 24r2s7 + 72r3s4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6r2s3'.
6r2s3(-1 + 4s4 + 12rs) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'r2s3' equal to zero and attempt to solve:

Simplifying
r2s3 = 0

Solving
r2s3 = 0

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

Simplifying
r2s3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + 4s4 + 12rs)' equal to zero and attempt to solve:

Simplifying
-1 + 4s4 + 12rs = 0

Reorder the terms:
-1 + 12rs + 4s4 = 0

Solving
-1 + 12rs + 4s4 = 0

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

Add '1' to each side of the equation.
-1 + 12rs + 1 + 4s4 = 0 + 1

Reorder the terms:
-1 + 1 + 12rs + 4s4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 12rs + 4s4 = 0 + 1
12rs + 4s4 = 0 + 1

Combine like terms: 0 + 1 = 1
12rs + 4s4 = 1

Add '-4s4' to each side of the equation.
12rs + 4s4 + -4s4 = 1 + -4s4

Combine like terms: 4s4 + -4s4 = 0
12rs + 0 = 1 + -4s4
12rs = 1 + -4s4

Divide each side by '12s'.
r = 0.08333333333s-1 + -0.3333333333s3

Simplifying
r = 0.08333333333s-1 + -0.3333333333s3
Solution
r = {0.08333333333s-1 + -0.3333333333s3}