r^4+5r^3=6r^2

Solution for r^4+5r^3=6r^2 equation:

Simplifying
r4 + 5r3 = 6r2

Reorder the terms:
5r3 + r4 = 6r2

Solving
5r3 + r4 = 6r2

Solving for variable 'r'.

Reorder the terms:
-6r2 + 5r3 + r4 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
-6r2 + 5r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-6 + 5r + r2) = 0

Factor a trinomial.
r2((-6 + -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 '(-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
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, -6, 1}