=3r^4-r^3t-4r^2t^2+6rt^2+4r^2t^2-4rt^3

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Solution for =3r^4-r^3t-4r^2t^2+6rt^2+4r^2t^2-4rt^3 equation: 


Simplifying
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + -4rt3

Reorder the terms:
0 = 6rt2 + -4rt3 + -4r2t2 + 4r2t2 + -1r3t + 3r4

Combine like terms: -4r2t2 + 4r2t2 = 0
0 = 6rt2 + -4rt3 + 0 + -1r3t + 3r4
0 = 6rt2 + -4rt3 + -1r3t + 3r4

Solving
0 = 6rt2 + -4rt3 + -1r3t + 3r4

Solving for variable 'r'.
Remove the zero:
-6rt2 + 4rt3 + r3t + -3r4 = 6rt2 + -4rt3 + -1r3t + 3r4 + -6rt2 + 4rt3 + r3t + -3r4

Reorder the terms:
-6rt2 + 4rt3 + r3t + -3r4 = 6rt2 + -6rt2 + -4rt3 + 4rt3 + -1r3t + r3t + 3r4 + -3r4

Combine like terms: 6rt2 + -6rt2 = 0
-6rt2 + 4rt3 + r3t + -3r4 = 0 + -4rt3 + 4rt3 + -1r3t + r3t + 3r4 + -3r4
-6rt2 + 4rt3 + r3t + -3r4 = -4rt3 + 4rt3 + -1r3t + r3t + 3r4 + -3r4

Combine like terms: -4rt3 + 4rt3 = 0
-6rt2 + 4rt3 + r3t + -3r4 = 0 + -1r3t + r3t + 3r4 + -3r4
-6rt2 + 4rt3 + r3t + -3r4 = -1r3t + r3t + 3r4 + -3r4

Combine like terms: -1r3t + r3t = 0
-6rt2 + 4rt3 + r3t + -3r4 = 0 + 3r4 + -3r4
-6rt2 + 4rt3 + r3t + -3r4 = 3r4 + -3r4

Combine like terms: 3r4 + -3r4 = 0
-6rt2 + 4rt3 + r3t + -3r4 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-6t2 + 4t3 + r2t + -3r3) = 0


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 '(-6t2 + 4t3 + r2t + -3r3)' equal to zero and attempt to solve:

Simplifying
-6t2 + 4t3 + r2t + -3r3 = 0

Reorder the terms:
r2t + -3r3 + -6t2 + 4t3 = 0

Solving
r2t + -3r3 + -6t2 + 4t3 = 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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