First you multiply the last term by the first term (3h+16h+15). Then find numbers that add to 16 and multiply to 15 then add or subtract it from (3h+15)(3h+1). Then factor if possible (h+5)(3h+1)
G(p+4)=3(p+4)^2+2(p+4)+27
=3p^2+24p+48+2p+8+27
=3p^2+26p+83