r(r+2)(r-1)=0

Solution for r(r+2)(r-1)=0 equation:

Simplifying
r(r + 2)(r + -1) = 0

Reorder the terms:
r(2 + r)(r + -1) = 0

Reorder the terms:
r(2 + r)(-1 + r) = 0

Multiply (2 + r) * (-1 + r)
r(2(-1 + r) + r(-1 + r)) = 0
r((-1 * 2 + r * 2) + r(-1 + r)) = 0
r((-2 + 2r) + r(-1 + r)) = 0
r(-2 + 2r + (-1 * r + r * r)) = 0
r(-2 + 2r + (-1r + r2)) = 0

Combine like terms: 2r + -1r = 1r
r(-2 + 1r + r2) = 0
(-2 * r + 1r * r + r2 * r) = 0
(-2r + 1r2 + r3) = 0

Solving
-2r + 1r2 + r3 = 0

Solving for variable 'r'.

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

Factor a trinomial.
r((-2 + -1r)(1 + -1r)) = 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)' 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
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, -2, 1}