No need to try to shut the door behind you while you have your arms full anymore. Watch this DIY Self Closing Door Hinge Installation and Operation Instructional Tutorial and put one in yourself. It's easy. I'll post a link to some below. Simply remove the middle existing hinge on the door (leaving the upper and lower one in place) and install the self closing door hinge in it's place. It's easiest if you use a cordless drill for the hinge fasteners but not mandatory. You could do this with a regular handheld manual screwdriver. You will need the correct size Allen (hex head) wrench for the internal set screw to set the tension on the hinge. Some of the hinges will come with the correct size Allen wrench to use. You tighten the Allen screw inside the hinge to set the tension of the hinge on desired self-closing strength. You can always adjust it later if you find you don't like your settings. This video provides easy installation instructions to replace the middle door hinge with a self-closing door hinge and tension adjustment instructions.
Here is a set of them on amazon: https://amzn.to/2TTARK5