r^4+30r^2=11r^3

Solution for r^4+30r^2=11r^3 equation:

Simplifying
r4 + 30r2 = 11r3

Reorder the terms:
30r2 + r4 = 11r3

Solving
30r2 + r4 = 11r3

Solving for variable 'r'.

Reorder the terms:
30r2 + -11r3 + r4 = 11r3 + -11r3

Combine like terms: 11r3 + -11r3 = 0
30r2 + -11r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(30 + -11r + r2) = 0

Factor a trinomial.
r2((5 + -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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
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, 5, 6}