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

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


Simplifying
0 = -1r3 + -1r2 + 2r

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

Solving
0 = 2r + -1r2 + -1r3

Solving for variable 'r'.
Remove the zero:
-2r + r2 + r3 = 2r + -1r2 + -1r3 + -2r + r2 + r3

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

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

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

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

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}

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