The only functional root exploit I have found is via an obscure Chinese program called VROOT. While there is much speculation in other threads as to the nature of this program (and potential for malware), I have had success with it on multiple occasions where no other tool I tried worked. I have seen no evidence that it installs anything other than its strange app market (as an easily-removable user app!) and a superuser program called KingRoot (as a system app, where it should be). While it appears entirely benign and functional, I personally prefer to use superSU. Therefore, the below instructions will include the removal of KingRoot and installation of SuperSU in its place. It is assumed that you have ZTE's preloaded drivers installed and that you have confirmed adb is working.
Unfortunately, VROOT is a Windows-only application, though it works perfectly in a Windows virtual machine (that's how I use it!).
- Download VROOT and the newest SuperSU
- Install and run VROOT. It might take more than one try to succeed.
- Confirm that KingRoot is installed, and uninstall the 100% Chinese app that is also present. At this point, your device is rooted. You can simply keep KingRoot, but I would advise continuing to install superSU.
- Extract "common/Superuser.apk" from the downloaded SuperSU zip and install it on the device via adb or the file manager.
- Open SuperSU and grant it root permissions when KingRoot prompts you. Swipe over to the settings pane and select "Switch superuser app".
- Follow its instructions. After rebooting the device, simply install SuperSU again, open it, update the su binary when prompted, and select "Install SuperSU inte /system" from the settings pane. You're done!