What does "trivial solution" mean? What does "trivial solution" mean exactly?
Must the trivial solution always be equal to the zero-solution (where all unknowns/variables are zero)?

The etymology of the word "trivial " has to do with things that are commonly known.   Literally "three-way", like things that would be known by most people at a marketplace,  say, or anywhere where three paths come together. ..
Mike Spivak wrote that "when mathematics is done correctly it is trivial"  (in his book calculus on manifolds)...
