(2x^3z^4-8x^5)(-4xz^2)=0

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Solution for (2x^3z^4-8x^5)(-4xz^2)=0 equation: 


Simplifying
(2x3z4 + -8x5)(-4xz2) = 0

Remove parenthesis around (-4xz2)
(2x3z4 + -8x5) * -4xz2 = 0

Reorder the terms for easier multiplication:
-4xz2(2x3z4 + -8x5) = 0
(2x3z4 * -4xz2 + -8x5 * -4xz2) = 0
(-8x4z6 + 32x6z2) = 0

Solving
-8x4z6 + 32x6z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x4z2'.
8x4z2(-1z4 + 4x2) = 0

Factor a difference between two squares.
8x4z2((z2 + 2x)(-1z2 + 2x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x4z2' equal to zero and attempt to solve:

Simplifying
x4z2 = 0

Solving
x4z2 = 0

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

Simplifying
x4z2 = 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 '(z2 + 2x)' equal to zero and attempt to solve:

Simplifying
z2 + 2x = 0

Reorder the terms:
2x + z2 = 0

Solving
2x + z2 = 0

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

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

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

Divide each side by '2'.
x = -0.5z2

Simplifying
x = -0.5z2

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

Simplifying
-1z2 + 2x = 0

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

Solving
2x + -1z2 = 0

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

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

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

Divide each side by '2'.
x = 0.5z2

Simplifying
x = 0.5z2
Solution
x = {-0.5z2, 0.5z2}

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