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

Solution for Y(y+1)2(y-2)=0 equation:

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

Reorder the terms:
Y(1 + y) * 2(y + -2) = 0

Reorder the terms:
Y(1 + y) * 2(-2 + y) = 0

Reorder the terms for easier multiplication:
2Y(1 + y)(-2 + y) = 0

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

Combine like terms: 1y + -2y = -1y
2Y(-2 + -1y + y2) = 0
(-2 * 2Y + -1y * 2Y + y2 * 2Y) = 0
(-4Y + -2yY + 2y2Y) = 0

Solving
-4Y + -2yY + 2y2Y = 0

Solving for variable 'Y'.

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

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

Factor a trinomial.
2Y((-1 + -1y)(2 + -1y)) = 0

Ignore the factor 2.
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 + -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

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

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

Simplifying
0 = 1 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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

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

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

Simplifying
0 = -2 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
Y = {0}