r^4+4r^3=5r^2

Solution for r^4+4r^3=5r^2 equation:

Simplifying
r4 + 4r3 = 5r2

Reorder the terms:
4r3 + r4 = 5r2

Solving
4r3 + r4 = 5r2

Solving for variable 'r'.

Reorder the terms:
-5r2 + 4r3 + r4 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
-5r2 + 4r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-5 + 4r + r2) = 0

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {0, -5, 1}