The rhyzome is the stiff green part that runs horizontally, perpendicular to the leaves.
Whatever happens, make sure that part is never buried into the substrate. The brown roots function mainly to just attach themselves to driftwood and such, but it takes them a while to take hold. In my experience I found that young, developing plants attached themselves the most readily. The easiest method is to try to find nooks and crannies to wedge the roots/rhizome into, and then the plant will do the rest and develop roots that grab hold of the object.