r^4=2r^3+15r^2

Solution for r^4=2r^3+15r^2 equation:

Simplifying
r4 = 2r3 + 15r2

Reorder the terms:
r4 = 15r2 + 2r3

Solving
r4 = 15r2 + 2r3

Solving for variable 'r'.

Reorder the terms:
-15r2 + -2r3 + r4 = 15r2 + 2r3 + -15r2 + -2r3

Reorder the terms:
-15r2 + -2r3 + r4 = 15r2 + -15r2 + 2r3 + -2r3

Combine like terms: 15r2 + -15r2 = 0
-15r2 + -2r3 + r4 = 0 + 2r3 + -2r3
-15r2 + -2r3 + r4 = 2r3 + -2r3

Combine like terms: 2r3 + -2r3 = 0
-15r2 + -2r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-15 + -2r + r2) = 0

Factor a trinomial.
r2((-3 + -1r)(5 + -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 '(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
Solution
r = {0, -3, 5}