(3y)(4y-2)(4y+2)=

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Solution for (3y)(4y-2)(4y+2)= equation: 


Simplifying
(3y)(4y + -2)(4y + 2) = 0

Remove parenthesis around (3y)
3y(4y + -2)(4y + 2) = 0

Reorder the terms:
3y(-2 + 4y)(4y + 2) = 0

Reorder the terms:
3y(-2 + 4y)(2 + 4y) = 0

Multiply (-2 + 4y) * (2 + 4y)
3y(-2(2 + 4y) + 4y * (2 + 4y)) = 0
3y((2 * -2 + 4y * -2) + 4y * (2 + 4y)) = 0
3y((-4 + -8y) + 4y * (2 + 4y)) = 0
3y(-4 + -8y + (2 * 4y + 4y * 4y)) = 0
3y(-4 + -8y + (8y + 16y2)) = 0

Combine like terms: -8y + 8y = 0
3y(-4 + 0 + 16y2) = 0
3y(-4 + 16y2) = 0
(-4 * 3y + 16y2 * 3y) = 0
(-12y + 48y3) = 0

Solving
-12y + 48y3 = 0

Solving for variable 'y'.

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

Factor a difference between two squares.
12y((1 + 2y)(-1 + 2y)) = 0

Ignore the factor 12.

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 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5

Subproblem 3
Set the factor '(-1 + 2y)' equal to zero and attempt to solve:

Simplifying
-1 + 2y = 0

Solving
-1 + 2y = 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 + 2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2y = 0 + 1
2y = 0 + 1

Combine like terms: 0 + 1 = 1
2y = 1

Divide each side by '2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0, -0.5, 0.5}

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