r=r^4-2r^3+4r^2

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


Simplifying
r = r4 + -2r3 + 4r2

Reorder the terms:
r = 4r2 + -2r3 + r4

Solving
r = 4r2 + -2r3 + r4

Solving for variable 'r'.

Reorder the terms:
r + -4r2 + 2r3 + -1r4 = 4r2 + -4r2 + -2r3 + 2r3 + r4 + -1r4

Combine like terms: 4r2 + -4r2 = 0
r + -4r2 + 2r3 + -1r4 = 0 + -2r3 + 2r3 + r4 + -1r4
r + -4r2 + 2r3 + -1r4 = -2r3 + 2r3 + r4 + -1r4

Combine like terms: -2r3 + 2r3 = 0
r + -4r2 + 2r3 + -1r4 = 0 + r4 + -1r4
r + -4r2 + 2r3 + -1r4 = r4 + -1r4

Combine like terms: r4 + -1r4 = 0
r + -4r2 + 2r3 + -1r4 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(1 + -4r + 2r2 + -1r3) = 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 '(1 + -4r + 2r2 + -1r3)' equal to zero and attempt to solve:

Simplifying
1 + -4r + 2r2 + -1r3 = 0

Solving
1 + -4r + 2r2 + -1r3 = 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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