-4rs^5(8s^4-5r^2+6)=0

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Solution for -4rs^5(8s^4-5r^2+6)=0 equation: 


Simplifying
-4rs5(8s4 + -5r2 + 6) = 0

Reorder the terms:
-4rs5(6 + -5r2 + 8s4) = 0
(6 * -4rs5 + -5r2 * -4rs5 + 8s4 * -4rs5) = 0

Reorder the terms:
(-24rs5 + -32rs9 + 20r3s5) = 0
(-24rs5 + -32rs9 + 20r3s5) = 0

Solving
-24rs5 + -32rs9 + 20r3s5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4rs5'.
4rs5(-6 + -8s4 + 5r2) = 0

Factor a trinomial.
4rs5((-4s2 + -5r)(2s2 + -1r)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'rs5' equal to zero and attempt to solve:

Simplifying
rs5 = 0

Solving
rs5 = 0

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

Simplifying
rs5 = 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 '(-4s2 + -5r)' equal to zero and attempt to solve:

Simplifying
-4s2 + -5r = 0

Reorder the terms:
-5r + -4s2 = 0

Solving
-5r + -4s2 = 0

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

Add '4s2' to each side of the equation.
-5r + -4s2 + 4s2 = 0 + 4s2

Combine like terms: -4s2 + 4s2 = 0
-5r + 0 = 0 + 4s2
-5r = 0 + 4s2
Remove the zero:
-5r = 4s2

Divide each side by '-5'.
r = -0.8s2

Simplifying
r = -0.8s2

Subproblem 3
Set the factor '(2s2 + -1r)' equal to zero and attempt to solve:

Simplifying
2s2 + -1r = 0

Reorder the terms:
-1r + 2s2 = 0

Solving
-1r + 2s2 = 0

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

Add '-2s2' to each side of the equation.
-1r + 2s2 + -2s2 = 0 + -2s2

Combine like terms: 2s2 + -2s2 = 0
-1r + 0 = 0 + -2s2
-1r = 0 + -2s2
Remove the zero:
-1r = -2s2

Divide each side by '-1'.
r = 2s2

Simplifying
r = 2s2
Solution
r = {-0.8s2, 2s2}

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