Socket Coloring

I see most the bases are covered, but no one covered the jeweller orb method.

Take this case with Bronn's, to get 3R 2B 1G like you wanted, you can use the crafting bench recipe to first craft 3 sockets, and then craft 3R for starters. Next you can alternate between the 3 sockets and 4 sockets craft until you hit a blue socket on 4th socket, then alternate 4 and 5 sockets craft until you hit that 2nd blue, lastly do the 6th socket craft, which should almost always be green. After you got the colors all that's left to do will be to link the item (~1000 fusing or just craft 6L for 1500 fusing). The coloring step may take 1k~2k jeweller orbs depends on your luck, but this method is "doable" given how cheap both jewellers and fusings are, and should still be much cheaper than using chromes+fusing or buying a 6L 6 white socket Bronn's (only saw 1 listed for 7ex).

I also do agree with the others on how it may just be better to craft a rare chest. You can still get +1 levels, attack/spell crit, bunch of life and resist and other cool mods that should be better than a Bronn's for easier colors on a 6L. However, the jeweller's method is extremely useful and economical to get full off colors on 3 or 4 socket items.