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

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


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

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

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

Multiply (-4 + y) * (2 + y)
y(-4(2 + y) + y(2 + y)) = 0
y((2 * -4 + y * -4) + y(2 + y)) = 0
y((-8 + -4y) + y(2 + y)) = 0
y(-8 + -4y + (2 * y + y * y)) = 0
y(-8 + -4y + (2y + y2)) = 0

Combine like terms: -4y + 2y = -2y
y(-8 + -2y + y2) = 0
(-8 * y + -2y * y + y2 * y) = 0
(-8y + -2y2 + y3) = 0

Solving
-8y + -2y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8 + -2y + y2) = 0

Factor a trinomial.
y((-2 + -1y)(4 + -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 + -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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {0, -2, 4}

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