r^3-r^2+2r=0

Solution for r^3-r^2+2r=0 equation:

Simplifying
r3 + -1r2 + 2r = 0

Reorder the terms:
2r + -1r2 + r3 = 0

Solving
2r + -1r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(2 + -1r + r2) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(2 + -1r + r2)' equal to zero and attempt to solve:

Simplifying
2 + -1r + r2 = 0

Solving
2 + -1r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + -1r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r + r2 = 0 + -2
-1r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1r + r2 = -2

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = -2 + 0.25

Reorder the terms:
0.25 + -1r + r2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1r + r2 = -1.75

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}