-2r^6s^3(4s^2+9r-6)=

Solution for -2r^6s^3(4s^2+9r-6)= equation:

Simplifying
-2r6s3(4s2 + 9r + -6) = 0

Reorder the terms:
-2r6s3(-6 + 9r + 4s2) = 0
(-6 * -2r6s3 + 9r * -2r6s3 + 4s2 * -2r6s3) = 0

Reorder the terms:
(12r6s3 + -8r6s5 + -18r7s3) = 0
(12r6s3 + -8r6s5 + -18r7s3) = 0

Solving
12r6s3 + -8r6s5 + -18r7s3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r6s3'.
2r6s3(6 + -4s2 + -9r) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'r6s3' equal to zero and attempt to solve:

Simplifying
r6s3 = 0

Solving
r6s3 = 0

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

Simplifying
r6s3 = 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 '(6 + -4s2 + -9r)' equal to zero and attempt to solve:

Simplifying
6 + -4s2 + -9r = 0

Reorder the terms:
6 + -9r + -4s2 = 0

Solving
6 + -9r + -4s2 = 0

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

Add '-6' to each side of the equation.
6 + -9r + -6 + -4s2 = 0 + -6

Reorder the terms:
6 + -6 + -9r + -4s2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9r + -4s2 = 0 + -6
-9r + -4s2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9r + -4s2 = -6

Add '4s2' to each side of the equation.
-9r + -4s2 + 4s2 = -6 + 4s2

Combine like terms: -4s2 + 4s2 = 0
-9r + 0 = -6 + 4s2
-9r = -6 + 4s2

Divide each side by '-9'.
r = 0.6666666667 + -0.4444444444s2

Simplifying
r = 0.6666666667 + -0.4444444444s2
Solution
r = {0.6666666667 + -0.4444444444s2}