18r^3t^2+12r^2t^2-6r^2t=0

Solution for 18r^3t^2+12r^2t^2-6r^2t=0 equation:

Simplifying
18r3t2 + 12r2t2 + -6r2t = 0

Reorder the terms:
-6r2t + 12r2t2 + 18r3t2 = 0

Solving
-6r2t + 12r2t2 + 18r3t2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6r2t'.
6r2t(-1 + 2t + 3rt) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'r2t' equal to zero and attempt to solve:

Simplifying
r2t = 0

Solving
r2t = 0

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

Simplifying
r2t = 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 + 2t + 3rt)' equal to zero and attempt to solve:

Simplifying
-1 + 2t + 3rt = 0

Reorder the terms:
-1 + 3rt + 2t = 0

Solving
-1 + 3rt + 2t = 0

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

Add '1' to each side of the equation.
-1 + 3rt + 1 + 2t = 0 + 1

Reorder the terms:
-1 + 1 + 3rt + 2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3rt + 2t = 0 + 1
3rt + 2t = 0 + 1

Combine like terms: 0 + 1 = 1
3rt + 2t = 1

Add '-2t' to each side of the equation.
3rt + 2t + -2t = 1 + -2t

Combine like terms: 2t + -2t = 0
3rt + 0 = 1 + -2t
3rt = 1 + -2t

Divide each side by '3t'.
r = 0.3333333333t-1 + -0.6666666667

Simplifying
r = 0.3333333333t-1 + -0.6666666667

Reorder the terms:
r = -0.6666666667 + 0.3333333333t-1
Solution
r = {-0.6666666667 + 0.3333333333t-1}