Quote - As for how long it takes, i'll say this again, more then a language, you need to learn math. Languages are easy, anyone with half a brain can learn C/C++ in 6 months. Sure, you wont be a master but you can learn enough to make whatever programs you need to.

Being an experienced C/C++ programmer myself and having trained several C/C++ programmers I can say that teaching an experienced programmer to work properly in C/C++ takes at least 1 year when coached intensively (this doesn't mean they can't produce anything earlier but to write proper and efficient code takes time and experience). For a newby programmer (and this includes anyone just leaving any course or training, anyone who hasn't written commercial code for at least 2 years) add another year to understand that writing commercial code isn't about finding the best algorithm but about finding a proper compromise between functionality, flexibility and performance while keeping maintainability and testability in mind. In all I don't consider a C/C++ programmer with less than 4 years commercial experience an experienced programmer (and I do know several C/C++ programmers with far more experience than I don't consider worth their price).
As far as the math is concerned I know it is important but most of that part of the problem can be understood by working at it and trying out what will work for you. Begin simple and add complexity as you get to understanding it. First really understand the tools you use (this means the programming language and all development tools), then understand the problem you are trying to solve and then think about a simple solution, code it and refine it until it really works.
So this means for anyone starting with just dreams assume at least 8 years of full time work (or 12 years of after hours work). During the final 2 years you might find others willing to cooperate if your goal, code and documentation is clear and understandable.