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 + -2y2 + 2y3) = 0

Solving
-4y + -2y2 + 2y3 = 0

Solving for variable 'y'.

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

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

Simplifying
y = -1
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, -1, 2}