y(y-1)(2y+4)=0

Solution for y(y-1)(2y+4)=0 equation:

Simplifying
y(y + -1)(2y + 4) = 0

Reorder the terms:
y(-1 + y)(2y + 4) = 0

Reorder the terms:
y(-1 + y)(4 + 2y) = 0

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

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

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

Solving for variable 'y'.

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

Factor a trinomial.
2y((-2 + -1y)(1 + -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 '(-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
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
Solution
y = {0, -2, 1}