y(y+1)(y-1)(y+1)(y-1)=

Solution for y(y+1)(y-1)(y+1)(y-1)= equation:

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

Reorder the terms:
y(1 + y)(y + -1)(y + 1)(y + -1) = 0

Reorder the terms:
y(1 + y)(-1 + y)(y + 1)(y + -1) = 0

Reorder the terms:
y(1 + y)(-1 + y)(1 + y)(y + -1) = 0

Reorder the terms:
y(1 + y)(-1 + y)(1 + y)(-1 + y) = 0

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

Combine like terms: 1y + -1y = 0
y(-1 + 0 + y2)(1 + y)(-1 + y) = 0
y(-1 + y2)(1 + y)(-1 + y) = 0

Multiply (-1 + y2) * (1 + y)
y(-1(1 + y) + y2(1 + y))(-1 + y) = 0
y((1 * -1 + y * -1) + y2(1 + y))(-1 + y) = 0
y((-1 + -1y) + y2(1 + y))(-1 + y) = 0
y(-1 + -1y + (1 * y2 + y * y2))(-1 + y) = 0
y(-1 + -1y + (1y2 + y3))(-1 + y) = 0
y(-1 + -1y + 1y2 + y3)(-1 + y) = 0

Multiply (-1 + -1y + 1y2 + y3) * (-1 + y)
y(-1(-1 + y) + -1y * (-1 + y) + 1y2 * (-1 + y) + y3(-1 + y)) = 0
y((-1 * -1 + y * -1) + -1y * (-1 + y) + 1y2 * (-1 + y) + y3(-1 + y)) = 0
y((1 + -1y) + -1y * (-1 + y) + 1y2 * (-1 + y) + y3(-1 + y)) = 0
y(1 + -1y + (-1 * -1y + y * -1y) + 1y2 * (-1 + y) + y3(-1 + y)) = 0
y(1 + -1y + (1y + -1y2) + 1y2 * (-1 + y) + y3(-1 + y)) = 0
y(1 + -1y + 1y + -1y2 + (-1 * 1y2 + y * 1y2) + y3(-1 + y)) = 0
y(1 + -1y + 1y + -1y2 + (-1y2 + 1y3) + y3(-1 + y)) = 0
y(1 + -1y + 1y + -1y2 + -1y2 + 1y3 + (-1 * y3 + y * y3)) = 0
y(1 + -1y + 1y + -1y2 + -1y2 + 1y3 + (-1y3 + y4)) = 0

Combine like terms: -1y + 1y = 0
y(1 + 0 + -1y2 + -1y2 + 1y3 + -1y3 + y4) = 0
y(1 + -1y2 + -1y2 + 1y3 + -1y3 + y4) = 0

Combine like terms: -1y2 + -1y2 = -2y2
y(1 + -2y2 + 1y3 + -1y3 + y4) = 0

Combine like terms: 1y3 + -1y3 = 0
y(1 + -2y2 + 0 + y4) = 0
y(1 + -2y2 + y4) = 0
(1 * y + -2y2 * y + y4 * y) = 0
(1y + -2y3 + y5) = 0

Solving
1y + -2y3 + y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + -2y2 + y4) = 0

Factor a trinomial.
y((1 + -1y2)(1 + -1y2)) = 0

Factor a difference between two squares.
y(((1 + y)(1 + -1y))(1 + -1y2)) = 0

Factor a difference between two squares.
y(((1 + y)(1 + -1y))(1 + y)(1 + -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 '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Subproblem 4
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Subproblem 5
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {0, -1, 1, -1, 1}