r^5-7r^4+12r^3=

Solution for r^5-7r^4+12r^3= equation:

Simplifying
r5 + -7r4 + 12r3 = 0

Reorder the terms:
12r3 + -7r4 + r5 = 0

Solving
12r3 + -7r4 + r5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r3'.
r3(12 + -7r + r2) = 0

Factor a trinomial.
r3((3 + -1r)(4 + -1r)) = 0

Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve:

Simplifying
r3 = 0

Solving
r3 = 0

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

Simplifying
r3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {3, 4}