r^4+r^3+r^2=0

Solution for r^4+r^3+r^2=0 equation:

Simplifying
r4 + r3 + r2 = 0

Reorder the terms:
r2 + r3 + r4 = 0

Solving
r2 + r3 + r4 = 0

Solving for variable 'r'.

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

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 '(1 + r + r2)' equal to zero and attempt to solve:

Simplifying
1 + r + r2 = 0

Solving
1 + r + r2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The r term is r.  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.
r + 0.25 + r2 = -1 + 0.25

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

Combine like terms: -1 + 0.25 = -0.75
0.25 + r + r2 = -0.75

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = -0.75

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}