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

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


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

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

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

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

Combine like terms: -2y + -4y = -6y
y(8 + -6y + y2) = 0
(8 * y + -6y * y + y2 * y) = 0
(8y + -6y2 + y3) = 0

Solving
8y + -6y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(8 + -6y + 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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