r^4=3r^3+18r^2

Solution for r^4=3r^3+18r^2 equation:

Simplifying
r4 = 3r3 + 18r2

Reorder the terms:
r4 = 18r2 + 3r3

Solving
r4 = 18r2 + 3r3

Solving for variable 'r'.

Reorder the terms:
-18r2 + -3r3 + r4 = 18r2 + 3r3 + -18r2 + -3r3

Reorder the terms:
-18r2 + -3r3 + r4 = 18r2 + -18r2 + 3r3 + -3r3

Combine like terms: 18r2 + -18r2 = 0
-18r2 + -3r3 + r4 = 0 + 3r3 + -3r3
-18r2 + -3r3 + r4 = 3r3 + -3r3

Combine like terms: 3r3 + -3r3 = 0
-18r2 + -3r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-18 + -3r + r2) = 0

Factor a trinomial.
r2((-3 + -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 '(-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 '(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, -3, 6}