An "answer to" is more specific than an "answer about". Let me illustrate from a Trip Advisor post I just googled, which reads:
"I am trying to find out an answer about mattress firmness in this hotel."
The writer is seeking information about how firm the mattresses are there. Are they so soft that they will cause his bad back to become worse? He's trying to collect general feedback on what it was like to sleep in a bed at that hotel.
If he were investigating the mystery of why mattresses at that specific hotel were of a particular firmness, or perhaps how to adjust the mattress after he already had booked a room there, he would write that he was "trying to find out an answer to mattress firmness in this hotel".