Product of Roots of Sums of Products of Differences

Algebra Level 3

What is the product of all roots to the equation

\[ \begin{align} & (x-1)(x-2)(x-3) + (x-2)(x-3)(x-4) \\ + & (x-3)(x-4)(x-5) + (x-4)(x-5)(x-6) \\ + & (x-5)(x-6)(x-7) + (x-6)(x-7)(x-8) =0 ? \end{align} \]

Details and assumptions

Clarification: Make sure you scroll to the right (if need be) to see the full equation. This problem ends with a "?".

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