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Hello~everyone.

I'm English learner as a second language.

I know 'gonna' is the short of 'going to'

so people use it like 'we're gonna' or 'he's gonna' in the sentences.

but what about 'you can gonna'?

actually in the right grammar, it's not appropriate that we say 'gonna' after 'can'.

Isn't it right that we should use 'gonna' after 'be-verb'?

Please tell me the use of yours who lives in the place where people speak english as a first language.
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Gonna is extremely informal [some would say sub-standard, at least in writing], so there are no hard rules for its use. I would use it, in speaking, only before a bare infinitive (as you said, it replaces 'going to'). It is often preceded by 'a': I'm a-gonna do this or that.
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You cannot use 'going to' after 'can'.

You can use 'going to' after 'be'.

'Gonna' is not a word; it is simply an alphabetic transcription of a common pronunciation of 'going to'.