r^4=2r^3+24r^2

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Solution for r^4=2r^3+24r^2 equation: 


Simplifying
r4 = 2r3 + 24r2

Reorder the terms:
r4 = 24r2 + 2r3

Solving
r4 = 24r2 + 2r3

Solving for variable 'r'.

Reorder the terms:
-24r2 + -2r3 + r4 = 24r2 + 2r3 + -24r2 + -2r3

Reorder the terms:
-24r2 + -2r3 + r4 = 24r2 + -24r2 + 2r3 + -2r3

Combine like terms: 24r2 + -24r2 = 0
-24r2 + -2r3 + r4 = 0 + 2r3 + -2r3
-24r2 + -2r3 + r4 = 2r3 + -2r3

Combine like terms: 2r3 + -2r3 = 0
-24r2 + -2r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-24 + -2r + r2) = 0

Factor a trinomial.
r2((-4 + -1r)(6 + -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 '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {0, -4, 6}

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