In your Case, the correct choice in your case is “It turned out to be much simpler than I had thought” The correct choice in your case and in any case if you think that it proved to be “or maybe it was… more complicated than I thought and I was just trying to pass those tests” Then, you choose “that” and “than”, now. (Notice, not “that”, only”). This means that you discovered that the thing was simple.

Someone showed up physically. Is it about to turn up again? My sister didn’t to turn up at my birthday party. The results were like “My mother wasn’t at our party” means that she didn’t come to my birthday party. I believe my sweater will turn me to the store for repacking or “The sweater has turned up in my mail”. I thought I lost it, but I found it in the laundry. I have a million dollars in my sock.

Both of those verbs have other meanings too, but the ones I give here are very common in everyday speach.