My school days (here in the UK) are long behind me, but I can't help feeling that a lot of the blame can be ascribed to teaching methods. In 'the old days' it was often by rote, nowadays it's more often teaching to pass exams. I was lucky that my Dad loved maths (he used to do algebra problems as a hobby).
Where I think it could be improved is in relating maths to real life. Just as a very basic example, off the top of my head, 'how much paint do I need to buy to paint this room?'. Given that the tin will show 'average coverage' and calculating the area of the walls and ceiling is simple, it 's not hard. But I bet that a random poll would reveal that more people than you might think couldn't manage it.
(ETA): Farkel: enjoyed your succinct explanation of equations. I suspect that teachers may have more success if they employed your method!