(4xy-2x)(4xy+2x)=0

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


Simplifying
(4xy + -2x)(4xy + 2x) = 0

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

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

Multiply (-2x + 4xy) * (2x + 4xy)
(-2x * (2x + 4xy) + 4xy * (2x + 4xy)) = 0
((2x * -2x + 4xy * -2x) + 4xy * (2x + 4xy)) = 0
((-4x2 + -8x2y) + 4xy * (2x + 4xy)) = 0
(-4x2 + -8x2y + (2x * 4xy + 4xy * 4xy)) = 0
(-4x2 + -8x2y + (8x2y + 16x2y2)) = 0

Combine like terms: -8x2y + 8x2y = 0
(-4x2 + 0 + 16x2y2) = 0
(-4x2 + 16x2y2) = 0

Solving
-4x2 + 16x2y2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-1 + 4y2) = 0

Factor a difference between two squares.
4x2((1 + 2y)(-1 + 2y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {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 x 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

Add '-2y' to each side of the equation.
2y + -2y = -1 + -2y

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

Simplifying
0 = -1 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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 x 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

Add '-2y' to each side of the equation.
2y + -2y = 1 + -2y

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

Simplifying
0 = 1 + -2y

The solution to this equation could not be determined.

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

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