y^4+2y^3+2y^2=0

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

Simplifying
y4 + 2y3 + 2y2 = 0

Reorder the terms:
2y2 + 2y3 + y4 = 0

Solving
2y2 + 2y3 + y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(2 + 2y + y2) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(2 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
2 + 2y + y2 = 0

Solving
2 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 2y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2y + y2 = 0 + -2
2y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
2y + y2 = -2

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

Add '1' to each side of the equation.
2y + 1 + y2 = -2 + 1

Reorder the terms:
1 + 2y + y2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2y + y2 = -1

Factor a perfect square on the left side:
(y + 1)(y + 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
y = {0}