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

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

Simplifying
r2 + -2r3 + 3r2 = 0

Reorder the terms:
r2 + 3r2 + -2r3 = 0

Combine like terms: r2 + 3r2 = 4r2
4r2 + -2r3 = 0

Solving
4r2 + -2r3 = 0

Solving for variable 'r'.

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

Ignore the factor 2.
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 '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0, 2}