r^4=4r^3+21r^2

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Solution for r^4=4r^3+21r^2 equation: 


Simplifying
r4 = 4r3 + 21r2

Reorder the terms:
r4 = 21r2 + 4r3

Solving
r4 = 21r2 + 4r3

Solving for variable 'r'.

Reorder the terms:
-21r2 + -4r3 + r4 = 21r2 + 4r3 + -21r2 + -4r3

Reorder the terms:
-21r2 + -4r3 + r4 = 21r2 + -21r2 + 4r3 + -4r3

Combine like terms: 21r2 + -21r2 = 0
-21r2 + -4r3 + r4 = 0 + 4r3 + -4r3
-21r2 + -4r3 + r4 = 4r3 + -4r3

Combine like terms: 4r3 + -4r3 = 0
-21r2 + -4r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-21 + -4r + r2) = 0

Factor a trinomial.
r2((-3 + -1r)(7 + -1r)) = 0


Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}

Subproblem 2
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

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

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

Divide each side by '-1'.
r = -3

Simplifying
r = -3

Subproblem 3
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0, -3, 7}

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