How to fix this heavy shelving unit to solid supporting wall?
A Z bar hanger may work well. The lower half is fixed to the wall; the upper half is fixed to the object. Caveat: walls are sometimes not a flat plane, but instead have some curve to them. Use a straight edge to confirm your wall is flat where the mounting bar would go. If it isn't then it can be corrected by inserting shims behind the bar. (image credit: http://www.zbarhanger.com)



The bar will carry the weight of the cabinet with no trouble but it may be a good idea to use a few more fasteners directly through the cabinet into the wall, especially in the lower part of the cabinet. These would prevent the bottom of the cabinet being lifted away from the wall, the cabinet being slid sideways, or the cabinet being bumped upward enough to disengage the mounting bar.