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

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

Simplifying
r3 + 2r2 + 2r = 0

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

Solving
2r + 2r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(2 + 2r + 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 + 2r + r2)' equal to zero and attempt to solve:

Simplifying
2 + 2r + r2 = 0

Solving
2 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

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

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

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

Factor a perfect square on the left side:
(r + 1)(r + 1) = -1

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}