12r^4s^2+6r^3s^2-6r^2s^2=0

Solution for 12r^4s^2+6r^3s^2-6r^2s^2=0 equation:

Simplifying
12r4s2 + 6r3s2 + -6r2s2 = 0

Reorder the terms:
-6r2s2 + 6r3s2 + 12r4s2 = 0

Solving
-6r2s2 + 6r3s2 + 12r4s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6r2s2'.
6r2s2(-1 + r + 2r2) = 0

Factor a trinomial.
6r2s2((-1 + -1r)(1 + -2r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'r2s2' equal to zero and attempt to solve:

Simplifying
r2s2 = 0

Solving
r2s2 = 0

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

Simplifying
r2s2 = 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 + -1r)' equal to zero and attempt to solve:

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1r = 0 + 1
-1r = 0 + 1

Combine like terms: 0 + 1 = 1
-1r = 1

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

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-1, 0.5}