...
select * FROM `events` WHERE `status` = 0 AND `type` IN ("public", "private");
Eloquent:
$events = Event::where('status', 0)
->whereIn('type', ['public', 'private'])
->get();
OR/AND, :
$events = Event::where('status', 0)
->where(function($query) {
$query->where('type', 'public')
->orWhere('type', 'private');
})->get();