-5r^2(r-3r^2+2rt)=

Solution for -5r^2(r-3r^2+2rt)= equation:

Simplifying
-5r2(r + -3r2 + 2rt) = 0

Reorder the terms:
-5r2(r + 2rt + -3r2) = 0
(r * -5r2 + 2rt * -5r2 + -3r2 * -5r2) = 0
(-5r3 + -10r3t + 15r4) = 0

Solving
-5r3 + -10r3t + 15r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r3'.
5r3(-1 + -2t + 3r) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve:

Simplifying
r3 = 0

Solving
r3 = 0

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

Simplifying
r3 = 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 + 3r)' equal to zero and attempt to solve:

Simplifying
-1 + -2t + 3r = 0

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

Solving
-1 + 3r + -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 + 3r + 1 + -2t = 0 + 1

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

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

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

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

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

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

Simplifying
r = 0.3333333333 + 0.6666666667t
Solution
r = {0.3333333333 + 0.6666666667t}