$(45$ points$)$ Plot the Root Locus for the following loop gain function; include only initial pole$/$zero locations, loci on the real axis, asymptotes and their intersection location:

$G(s)H(s)=\frac{s+15}{(s+8)(s+6)(s+6+10j)(s+6-10j)}=\frac{s+15}{s^4+26s^3+352s^2+2480s+6528}$