z(5x-8)(z+4)=0

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Solution for z(5x-8)(z+4)=0 equation: 


Simplifying
z(5x + -8)(z + 4) = 0

Reorder the terms:
z(-8 + 5x)(z + 4) = 0

Reorder the terms:
z(-8 + 5x)(4 + z) = 0

Multiply (-8 + 5x) * (4 + z)
z(-8(4 + z) + 5x * (4 + z)) = 0
z((4 * -8 + z * -8) + 5x * (4 + z)) = 0
z((-32 + -8z) + 5x * (4 + z)) = 0
z(-32 + -8z + (4 * 5x + z * 5x)) = 0
z(-32 + -8z + (20x + 5xz)) = 0

Reorder the terms:
z(-32 + 20x + 5xz + -8z) = 0
z(-32 + 20x + 5xz + -8z) = 0
(-32 * z + 20x * z + 5xz * z + -8z * z) = 0

Reorder the terms:
(20xz + 5xz2 + -32z + -8z2) = 0
(20xz + 5xz2 + -32z + -8z2) = 0

Solving
20xz + 5xz2 + -32z + -8z2 = 0

Solving for variable 'x'.

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

Add '32z' to each side of the equation.
20xz + 5xz2 + -32z + 32z + -8z2 = 0 + 32z

Combine like terms: -32z + 32z = 0
20xz + 5xz2 + 0 + -8z2 = 0 + 32z
20xz + 5xz2 + -8z2 = 0 + 32z
Remove the zero:
20xz + 5xz2 + -8z2 = 32z

Add '8z2' to each side of the equation.
20xz + 5xz2 + -8z2 + 8z2 = 32z + 8z2

Combine like terms: -8z2 + 8z2 = 0
20xz + 5xz2 + 0 = 32z + 8z2
20xz + 5xz2 = 32z + 8z2

Reorder the terms:
20xz + 5xz2 + -32z + -8z2 = 32z + -32z + 8z2 + -8z2

Combine like terms: 32z + -32z = 0
20xz + 5xz2 + -32z + -8z2 = 0 + 8z2 + -8z2
20xz + 5xz2 + -32z + -8z2 = 8z2 + -8z2

Combine like terms: 8z2 + -8z2 = 0
20xz + 5xz2 + -32z + -8z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(20x + 5xz + -32 + -8z) = 0


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

Simplifying
z = 0

Solving
z = 0

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

Add '-1z' to each side of the equation.
z + -1z = 0 + -1z
Remove the zero:
0 = -1z

Simplifying
0 = -1z

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 '(20x + 5xz + -32 + -8z)' equal to zero and attempt to solve:

Simplifying
20x + 5xz + -32 + -8z = 0

Reorder the terms:
-32 + 20x + 5xz + -8z = 0

Solving
-32 + 20x + 5xz + -8z = 0

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

Add '32' to each side of the equation.
-32 + 20x + 5xz + 32 + -8z = 0 + 32

Reorder the terms:
-32 + 32 + 20x + 5xz + -8z = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 20x + 5xz + -8z = 0 + 32
20x + 5xz + -8z = 0 + 32

Combine like terms: 0 + 32 = 32
20x + 5xz + -8z = 32

Add '8z' to each side of the equation.
20x + 5xz + -8z + 8z = 32 + 8z

Combine like terms: -8z + 8z = 0
20x + 5xz + 0 = 32 + 8z
20x + 5xz = 32 + 8z

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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