y(2-y)(2+y)=0

Solution for y(2-y)(2+y)=0 equation:

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

Multiply (2 + -1y) * (2 + y)
y(2(2 + y) + -1y * (2 + y)) = 0
y((2 * 2 + y * 2) + -1y * (2 + y)) = 0
y((4 + 2y) + -1y * (2 + y)) = 0
y(4 + 2y + (2 * -1y + y * -1y)) = 0
y(4 + 2y + (-2y + -1y2)) = 0

Combine like terms: 2y + -2y = 0
y(4 + 0 + -1y2) = 0
y(4 + -1y2) = 0
(4 * y + -1y2 * y) = 0
(4y + -1y3) = 0

Solving
4y + -1y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(4 + -1y2) = 0

Factor a difference between two squares.
y((2 + y)(2 + -1y)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0, -2, 2}