8x^2z^2-4xz^2-12x^2=0

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Solution for 8x^2z^2-4xz^2-12x^2=0 equation: 


Simplifying
8x2z2 + -4xz2 + -12x2 = 0

Reorder the terms:
-4xz2 + -12x2 + 8x2z2 = 0

Solving
-4xz2 + -12x2 + 8x2z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1z2 + -3x + 2xz2) = 0

Ignore the factor 4.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1z2 + -3x + 2xz2)' equal to zero and attempt to solve:

Simplifying
-1z2 + -3x + 2xz2 = 0

Reorder the terms:
-3x + 2xz2 + -1z2 = 0

Solving
-3x + 2xz2 + -1z2 = 0

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

Add 'z2' to each side of the equation.
-3x + 2xz2 + -1z2 + z2 = 0 + z2

Combine like terms: -1z2 + z2 = 0
-3x + 2xz2 + 0 = 0 + z2
-3x + 2xz2 = 0 + z2
Remove the zero:
-3x + 2xz2 = z2

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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