The article states that before a noun, nuevo means newly acquired, but after it newly made. Surely starting a new business implies that the business did not previously exist and that it is therefore "newly made", so nuevo should come after the noun, or is it not as straightforward as that?
In addition, someone in another discussion explained that "nuevo negocio" means a business in addition to one(s) I already have, while "negocio nuevo" means a business that hasn't existed before. The difference was a little bit clearer with "nuevo trabajo" and "trabajo nuevo."
To clarify what I think you mean. Comenzar and empezar should both be allowed. I agree. In English they are different. In Spanish they are the same. https://study.com/academy/lesson/comenzar-vs-empezar.html
I tried different sentences in Google Translate to see what happens when using the word "nuevo" and different nouns. All the sentences that I tried put the adjective after the noun, except for "negocio". Interesting.
Update--I found this on a similar post--https://www.spanishdict.com/guide/adjective-placement Thank you user howcheng.
The adjective does not always come after the noun. Some adjectives, including nuevo, can also come before it. A list of such adjectives is provided at https://www.spanishdict.com/answers/100027/adjective-placement. Another relevant article is to be found at https://www.thoughtco.com/placement-of-some-adjectives-can-affect-their-meaning-3079080.
As far as I am concerned though, in the case of nuevo, neither link explains fully why nuevo comes before the noun in this sentence. The second article does however state:
And in some cases, as with nuevo, placement can also be a matter of emphasis rather than simply of meaning
which perhaps explains why nuevo comes before the noun in this sentence.
My husband explained this sentence could be related to doing some business.. like say running errands. (Negocio meaning errands could be a dialect thing.) But, in this context the nuevo would come before to indicate he's got some new business/errands/tasks to attend to. This supports the explanation of emphasis on the new.
Admiral and Elpa, adjective placement in Spanish isn't completely clear cut. Here are a couple of sites that may be helpful: https://www.spanishdict.com/guide/adjective-placement and https://users.pfw.edu/jehle/courses/ADJECT.HTM
I disagree. In english maybe, but not in spanish. https://study.com/academy/lesson/comenzar-vs-empezar.html