y(2y-8)(2y+6)=0

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Solution for y(2y-8)(2y+6)=0 equation: 


Simplifying
y(2y + -8)(2y + 6) = 0

Reorder the terms:
y(-8 + 2y)(2y + 6) = 0

Reorder the terms:
y(-8 + 2y)(6 + 2y) = 0

Multiply (-8 + 2y) * (6 + 2y)
y(-8(6 + 2y) + 2y * (6 + 2y)) = 0
y((6 * -8 + 2y * -8) + 2y * (6 + 2y)) = 0
y((-48 + -16y) + 2y * (6 + 2y)) = 0
y(-48 + -16y + (6 * 2y + 2y * 2y)) = 0
y(-48 + -16y + (12y + 4y2)) = 0

Combine like terms: -16y + 12y = -4y
y(-48 + -4y + 4y2) = 0
(-48 * y + -4y * y + 4y2 * y) = 0
(-48y + -4y2 + 4y3) = 0

Solving
-48y + -4y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-12 + -1y + y2) = 0

Factor a trinomial.
4y((-3 + -1y)(4 + -1y)) = 0

Ignore the factor 4.

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 '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

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, -3, 4}

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