(4xy-2z)(4xy-2z)=0

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


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

Multiply (4xy + -2z) * (4xy + -2z)
(4xy * (4xy + -2z) + -2z * (4xy + -2z)) = 0
((4xy * 4xy + -2z * 4xy) + -2z * (4xy + -2z)) = 0

Reorder the terms:
((-8xyz + 16x2y2) + -2z * (4xy + -2z)) = 0
((-8xyz + 16x2y2) + -2z * (4xy + -2z)) = 0
(-8xyz + 16x2y2 + (4xy * -2z + -2z * -2z)) = 0
(-8xyz + 16x2y2 + (-8xyz + 4z2)) = 0

Reorder the terms:
(-8xyz + -8xyz + 16x2y2 + 4z2) = 0

Combine like terms: -8xyz + -8xyz = -16xyz
(-16xyz + 16x2y2 + 4z2) = 0

Solving
-16xyz + 16x2y2 + 4z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4xyz + 4x2y2 + z2) = 0

Factor a trinomial.
4((2xy + -1z)(2xy + -1z)) = 0

Ignore the factor 4.

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

Simplifying
2xy + -1z = 0

Solving
2xy + -1z = 0

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

Add 'z' to each side of the equation.
2xy + -1z + z = 0 + z

Combine like terms: -1z + z = 0
2xy + 0 = 0 + z
2xy = 0 + z
Remove the zero:
2xy = z

Divide each side by '2y'.
x = 0.5y-1z

Simplifying
x = 0.5y-1z

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

Simplifying
2xy + -1z = 0

Solving
2xy + -1z = 0

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

Add 'z' to each side of the equation.
2xy + -1z + z = 0 + z

Combine like terms: -1z + z = 0
2xy + 0 = 0 + z
2xy = 0 + z
Remove the zero:
2xy = z

Divide each side by '2y'.
x = 0.5y-1z

Simplifying
x = 0.5y-1z
Solution
x = {0.5y-1z, 0.5y-1z}

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