y=4x(x+2)y

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Solution for y=4x(x+2)y equation: 


Simplifying
y = 4x(x + 2) * y

Reorder the terms:
y = 4x(2 + x) * y

Reorder the terms for easier multiplication:
y = 4x * y(2 + x)

Multiply x * y
y = 4xy(2 + x)
y = (2 * 4xy + x * 4xy)
y = (8xy + 4x2y)

Solving
y = 8xy + 4x2y

Solving for variable 'y'.

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

Add '-8xy' to each side of the equation.
-8xy + y = 8xy + -8xy + 4x2y

Combine like terms: 8xy + -8xy = 0
-8xy + y = 0 + 4x2y
-8xy + y = 4x2y

Add '-4x2y' to each side of the equation.
-8xy + -4x2y + y = 4x2y + -4x2y

Combine like terms: 4x2y + -4x2y = 0
-8xy + -4x2y + y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8x + -4x2 + 1) = 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 '(-8x + -4x2 + 1)' equal to zero and attempt to solve:

Simplifying
-8x + -4x2 + 1 = 0

Reorder the terms:
1 + -8x + -4x2 = 0

Solving
1 + -8x + -4x2 = 0

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

Add '-1' to each side of the equation.
1 + -8x + -1 + -4x2 = 0 + -1

Reorder the terms:
1 + -1 + -8x + -4x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x + -4x2 = 0 + -1
-8x + -4x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8x + -4x2 = -1

Add '8x' to each side of the equation.
-8x + 8x + -4x2 = -1 + 8x

Combine like terms: -8x + 8x = 0
0 + -4x2 = -1 + 8x
-4x2 = -1 + 8x

Add '4x2' to each side of the equation.
-4x2 + 4x2 = -1 + 8x + 4x2

Combine like terms: -4x2 + 4x2 = 0
0 = -1 + 8x + 4x2

Simplifying
0 = -1 + 8x + 4x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}

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