(r-t)(r-t)(r-t)*5r=

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Solution for (r-t)(r-t)(r-t)*5r= equation: 


Simplifying
(r + -1t)(r + -1t)(r + -1t) * 5r = 0

Reorder the terms for easier multiplication:
5r(r + -1t)(r + -1t)(r + -1t) = 0

Multiply (r + -1t) * (r + -1t)
5r(r(r + -1t) + -1t * (r + -1t))(r + -1t) = 0
5r((r * r + -1t * r) + -1t * (r + -1t))(r + -1t) = 0

Reorder the terms:
5r((-1rt + r2) + -1t * (r + -1t))(r + -1t) = 0
5r((-1rt + r2) + -1t * (r + -1t))(r + -1t) = 0
5r(-1rt + r2 + (r * -1t + -1t * -1t))(r + -1t) = 0
5r(-1rt + r2 + (-1rt + 1t2))(r + -1t) = 0

Reorder the terms:
5r(-1rt + -1rt + r2 + 1t2)(r + -1t) = 0

Combine like terms: -1rt + -1rt = -2rt
5r(-2rt + r2 + 1t2)(r + -1t) = 0

Multiply (-2rt + r2 + 1t2) * (r + -1t)
5r(-2rt * (r + -1t) + r2(r + -1t) + 1t2 * (r + -1t)) = 0
5r((r * -2rt + -1t * -2rt) + r2(r + -1t) + 1t2 * (r + -1t)) = 0

Reorder the terms:
5r((2rt2 + -2r2t) + r2(r + -1t) + 1t2 * (r + -1t)) = 0
5r((2rt2 + -2r2t) + r2(r + -1t) + 1t2 * (r + -1t)) = 0
5r(2rt2 + -2r2t + (r * r2 + -1t * r2) + 1t2 * (r + -1t)) = 0

Reorder the terms:
5r(2rt2 + -2r2t + (-1r2t + r3) + 1t2 * (r + -1t)) = 0
5r(2rt2 + -2r2t + (-1r2t + r3) + 1t2 * (r + -1t)) = 0
5r(2rt2 + -2r2t + -1r2t + r3 + (r * 1t2 + -1t * 1t2)) = 0
5r(2rt2 + -2r2t + -1r2t + r3 + (1rt2 + -1t3)) = 0

Reorder the terms:
5r(2rt2 + 1rt2 + -2r2t + -1r2t + r3 + -1t3) = 0

Combine like terms: 2rt2 + 1rt2 = 3rt2
5r(3rt2 + -2r2t + -1r2t + r3 + -1t3) = 0

Combine like terms: -2r2t + -1r2t = -3r2t
5r(3rt2 + -3r2t + r3 + -1t3) = 0
(3rt2 * 5r + -3r2t * 5r + r3 * 5r + -1t3 * 5r) = 0

Reorder the terms:
(-5rt3 + 15r2t2 + -15r3t + 5r4) = 0
(-5rt3 + 15r2t2 + -15r3t + 5r4) = 0

Solving
-5rt3 + 15r2t2 + -15r3t + 5r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-1t3 + 3rt2 + -3r2t + r3) = 0

Ignore the factor 5.

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(-1t3 + 3rt2 + -3r2t + r3)' equal to zero and attempt to solve:

Simplifying
-1t3 + 3rt2 + -3r2t + r3 = 0

Reorder the terms:
3rt2 + -3r2t + r3 + -1t3 = 0

Solving
3rt2 + -3r2t + r3 + -1t3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}

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