Come across means to find something by chance, get across means to communicate an idea so people understand it, and bring about means to cause something to happen. All three are neutral in register, natural in both speech and writing, though bring about leans slightly formal and usually describes bigger changes like reforms or policies. Come across has a second, very common sense too: come across as + a describing word means to give an impression, she comes across as confident, it came across as rude. Watch the word order: come across is inseparable, so the object follows the whole verb ('come across an article', never 'come an article across'), while get across splits around a short object ('get your point across') but stays together when the object is long ('get across the idea that timing mattered').
Finding by chance and getting a point across
come across /kʌm əˈkrɔs/ — I came across a fascinating article on sleep while I was tidying my desk.
get across /ɡɛt əˈkrɔs/ — She used a simple diagram to get her point across to the whole room.
bring about /brɪŋ əˈbaʊt/ — The new manager brought about real changes in how the team works.
Not ""I came an interesting article across yesterday." (splits an inseparable verb)" — say ""I came across an interesting article yesterday." (object follows the whole verb)". Come across is inseparable, so the object goes after the particle. You can't slot it between 'come' and 'across'.
Try it: During the debate, I couldn't ___ my main point clearly. Which fits? (get across / come across / bring about) Answer: get across — 'Get across' means to communicate an idea successfully, which is what a debate point needs. 'Come across' is for finding something by chance, not communicating, and 'bring about' means to cause something to happen, not to express it.
Try it: The reforms were designed to ___ lasting change in the school system. Which fits? (bring about / get across / fall through) Answer: bring about — 'Bring about' means to cause something to happen, which fits reforms creating change. 'Get across' is for communicating an idea, not causing an outcome, and 'fall through' means to fail, the opposite of what reforms are meant to do.
Carrying on, falling through, and turning out
Use carry on to continue an activity, go over to check or review something carefully, fall through when a plan fails to happen, and turn out for how something finally results. All four are neutral and conversational — everyday in speech and informal writing. In connotation, fall through is negative (a plan collapses), while carry on and turn out are neutral; turn out often pairs with how good or bad the result was ('it turned out well').
carry on /ˈkæri ɑn/ — Despite the interruptions, they carried on working until the report was finished.
go over /goʊ ˈoʊvɚ/ — Let's go over the contract one more time before we sign it.
fall through /fɔl θru/ — The deal fell through at the last minute when the funding disappeared.
turn out /tɝn aʊt/ — The presentation turned out better than any of us expected.
Not ""The deal turned out at the last minute when the funding vanished." (uses 'turn out' for a plan that failed to happen)" — say ""The deal fell through at the last minute when the funding vanished." (a plan collapsing is 'fall through')". Fall through means a plan fails to happen; turn out describes how something finally results, not whether it happened. Don't use 'turn out' for a collapse.
Try it: We had booked the venue, but the whole event ___ when the sponsor pulled out. Which fits? (fell through / carried on / turned out) Answer: fell through — 'Fell through' means a plan failed to happen, which matches the sponsor pulling out and the event collapsing. 'Carried on' would mean it continued, the opposite of what happened, and 'turned out' would describe a result rather than a failure to occur.