(6x^2z^6-2x^4)(-8xz^3)=0

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Solution for (6x^2z^6-2x^4)(-8xz^3)=0 equation: 


Simplifying
(6x2z6 + -2x4)(-8xz3) = 0

Remove parenthesis around (-8xz3)
(6x2z6 + -2x4) * -8xz3 = 0

Reorder the terms for easier multiplication:
-8xz3(6x2z6 + -2x4) = 0
(6x2z6 * -8xz3 + -2x4 * -8xz3) = 0
(-48x3z9 + 16x5z3) = 0

Solving
-48x3z9 + 16x5z3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16x3z3'.
16x3z3(-3z6 + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor 'x3z3' equal to zero and attempt to solve:

Simplifying
x3z3 = 0

Solving
x3z3 = 0

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

Simplifying
x3z3 = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-3z6 + x2)' equal to zero and attempt to solve:

Simplifying
-3z6 + x2 = 0

Reorder the terms:
x2 + -3z6 = 0

Solving
x2 + -3z6 = 0

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

Add '3z6' to each side of the equation.
x2 + -3z6 + 3z6 = 0 + 3z6

Combine like terms: -3z6 + 3z6 = 0
x2 + 0 = 0 + 3z6
x2 = 0 + 3z6
Remove the zero:
x2 = 3z6

Simplifying
x2 = 3z6

Take the square root of each side:
x = {-1.732050808z3, 1.732050808z3}
Solution
x = {-1.732050808z3, 1.732050808z3}

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