To multiply the fractions
\[ \frac{8 - 2z}{25} \times \frac{50}{5z - 20}, \]
we start by simplifying each fraction and the product.
First, factor the numerator and denominator where possible.
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The first fraction is already in its lowest terms: \[ \frac{8 - 2z}{25}. \]
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For the second fraction, we can factor the denominator: \[ 5z - 20 = 5(z - 4). \] So the second fraction can be rewritten as: \[ \frac{50}{5(z - 4)}. \] We can simplify it: \[ \frac{50}{5(z - 4)} = \frac{10}{z - 4}. \]
Now, we have: \[ \frac{8 - 2z}{25} \times \frac{10}{z - 4}. \]
Next, we can simplify \(8 - 2z\). Notice that \(8 - 2z\) can be factored out: \[ 8 - 2z = 2(4 - z). \] So now, substituting back, we have: \[ \frac{2(4 - z)}{25} \times \frac{10}{z - 4}. \]
We know that \(4 - z = -(z - 4)\). This relationship allows us to rewrite the expression: \[ \frac{2(- (z - 4))}{25} \times \frac{10}{z - 4} = \frac{-2(z - 4)}{25} \times \frac{10}{z - 4}. \]
Now we can cancel \(z - 4\) (as long as \(z \neq 4\)): \[ = \frac{-2 \cdot 10}{25} = \frac{-20}{25}. \]
Finally, simplify \(\frac{-20}{25}\) to its lowest terms: \[ \frac{-20 \div 5}{25 \div 5} = \frac{-4}{5}. \]
Thus, the final answer is: \[ \boxed{\frac{-4}{5}}. \]