-32r^2s^4-8rs^4+36r^3s^4=

Solution for -32r^2s^4-8rs^4+36r^3s^4= equation:

Simplifying
-32r2s4 + -8rs4 + 36r3s4 = 0

Reorder the terms:
-8rs4 + -32r2s4 + 36r3s4 = 0

Solving
-8rs4 + -32r2s4 + 36r3s4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4rs4'.
4rs4(-2 + -8r + 9r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'rs4' equal to zero and attempt to solve:

Simplifying
rs4 = 0

Solving
rs4 = 0

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

Simplifying
rs4 = 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 '(-2 + -8r + 9r2)' equal to zero and attempt to solve:

Simplifying
-2 + -8r + 9r2 = 0

Solving
-2 + -8r + 9r2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-0.2222222222 + -0.8888888889r + r2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.8888888889r + 0.2222222222 + r2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.8888888889r + r2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.8888888889r + r2 = 0 + 0.2222222222
-0.8888888889r + r2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.8888888889r + r2 = 0.2222222222

The r term is -0.8888888889r.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889r + 0.1975308642 + r2 = 0.2222222222 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889r + r2 = 0.2222222222 + 0.1975308642

Combine like terms: 0.2222222222 + 0.1975308642 = 0.4197530864
0.1975308642 + -0.8888888889r + r2 = 0.4197530864

Factor a perfect square on the left side:
(r + -0.4444444445)(r + -0.4444444445) = 0.4197530864

Calculate the square root of the right side: 0.647883544

Break this problem into two subproblems by setting 
(r + -0.4444444445) equal to 0.647883544 and -0.647883544.

Subproblem 1
r + -0.4444444445 = 0.647883544

Simplifying
r + -0.4444444445 = 0.647883544

Reorder the terms:
-0.4444444445 + r = 0.647883544

Solving
-0.4444444445 + r = 0.647883544

Solving for variable 'r'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + r = 0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + r = 0.647883544 + 0.4444444445
r = 0.647883544 + 0.4444444445

Combine like terms: 0.647883544 + 0.4444444445 = 1.0923279885
r = 1.0923279885

Simplifying
r = 1.0923279885

Subproblem 2
r + -0.4444444445 = -0.647883544

Simplifying
r + -0.4444444445 = -0.647883544

Reorder the terms:
-0.4444444445 + r = -0.647883544

Solving
-0.4444444445 + r = -0.647883544

Solving for variable 'r'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + r = -0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + r = -0.647883544 + 0.4444444445
r = -0.647883544 + 0.4444444445

Combine like terms: -0.647883544 + 0.4444444445 = -0.2034390995
r = -0.2034390995

Simplifying
r = -0.2034390995

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.0923279885, -0.2034390995}
Solution
r = {1.0923279885, -0.2034390995}