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The left-hand side, when multiplied out, is a polynomial of degree $6.$ By Vieta's formulas, the product of the roots is determined by its $x^6$ coefficient and its constant term. The $x^6$ coefficient is $2\cdot 5=10$ and the constant term is $20\cdot 19=380,$ so the product of the roots is $\frac{380}{10}=\boxed{38}.$