There are two ways you can unlock an Android phone without damaging or deleting the data stored on it:
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Contact a local phone service or local ZTE representatives and they should unlock it for a small fee or for free, depends entirely if you have a contract or not.
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Actually entering the unlock data: PIN, pattern, email verification, etc.
I recommend trying the second method because is the safest one around, but if that doesn't work, visit a local phone service shop and they should do it for a small fee.