Installing linuxmint on C720p is pretty straightforward (except probably the little trick to make saebios and linux boot default).
Making the trackpad working is a little bit tricky mostly because installing procedures found around the web do not focus on linuxmint.
So here is a step by step procedure I followed.
download the Chrubuntu trackpad build script
make it executable withchmod 755
doapt-get update then apt-get upgrade
install the following dependencies :apt-get install build-dep linux-sources dpkg-source dpkg-dev
then try to launch./cros-haswell-modules.sh
reboot, it should work