jmc

By Vieta's formulas, the sum of the roots of $2x^3+x^2-8x+20=0$ is $-\frac{1}{2}.$ Similarly, the sum of the roots of $5x^3-25x^2+19=0$ is $-\frac{-25}{5}=5.$ Notice that the roots of the given equation consist of the roots of both equations put together (since, in general, $ab=0$ if and only if $a=0$ or $b=0$). Therefore, the sum of the roots of the given equation is $-\frac{1}{2}+5=\boxed{\frac{9}{2}}.$