From
start. The Columbia Guide to Standard American English. 1993
start (v.)
This weak verb can be combined with either a gerund or to plus an infinitive: He started speaking and He started to speak mean the same.
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Note, though, that for some native speakers there is a difference between
start to do and
start doing:
Start to do <hasn't started yet or is in preparation>
Ex:I'll start to do that tomorrow.
Start doing <has started already or is already prepared and ready to start>
Ex: I'll start doing that tomorrow.