r^4=3r^3+28r^2

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Solution for r^4=3r^3+28r^2 equation: 


Simplifying
r4 = 3r3 + 28r2

Reorder the terms:
r4 = 28r2 + 3r3

Solving
r4 = 28r2 + 3r3

Solving for variable 'r'.

Reorder the terms:
-28r2 + -3r3 + r4 = 28r2 + 3r3 + -28r2 + -3r3

Reorder the terms:
-28r2 + -3r3 + r4 = 28r2 + -28r2 + 3r3 + -3r3

Combine like terms: 28r2 + -28r2 = 0
-28r2 + -3r3 + r4 = 0 + 3r3 + -3r3
-28r2 + -3r3 + r4 = 3r3 + -3r3

Combine like terms: 3r3 + -3r3 = 0
-28r2 + -3r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-28 + -3r + r2) = 0

Factor a trinomial.
r2((-4 + -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 '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4

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, -4, 7}

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