I'll throw my own experiences out there, too.
I was homeschooled except for 6th-8th grade. I absolutely hated the public school experience, because most of the time there were things I was much more interested in doing than sitting at a desk doing boring things. Reading, for one.
But I also hated mathematics. Nobody could give me a good reason for why I should need to care about math, and I hated Saxon math (the homeschool math curriculum of choice, it seems like.) When I got to be homeschooled again, I would drag my feet a lot when it came to math, and by the time I was 16 I think my mom pretty much gave up on trying to get me to do math.
But at 16 I also took programming courses as the local tech college.
When I was 21, I finally decided it was time for college (well, actually it was really more some prodding from my parents, but I didn't really have anything better to do). I got a 25 composite on my ACT, with an 18 in math. Had my math scores been more in line with the rest of my scores I would have been closer to a 30 composite. That really wasn't anything new, though. My reading comprehension had always been in the high 80s-90 percentile. Science behind that.
So arguably I had really sucky grades.
However, when I started college I decided to give math a shot and discovered it was fun. I got almost all A's in my math classes, including Cal I, Cal II, and Linear Algebra. I ended out graduating with honors, even after taking 25 credit hours my final semester.
My problem? As a teenager I had a hard time seeing the benefit of learning things, like math. I didn't find it interesting, useful, or exciting. And honestly there are very few things about math that have been applicable to my life as a software developer - besides the general ability to take a look at a complex problem and break it down into less complicated parts.
I suspect that your child has the same issue - they're not motivated because they don't see how X, Y, or Z would be useful to them in their life, the things that they want to do.
What motivates your child? What causes their eyes to light up? What kinds of things do they do when they don't have anything to do?
Figure out how these other principles apply. And if you can't figure out how they apply, be honest. Just say, "You know what, being able to do multi-variable calculus probably won't make life as a fast-food clerk any better. But what it will do is show your employer that you will still do things that need to be done, even if they're not the exciting parts. And until you can pay your own bills, this is what we expect out of you."
Also, ask what they need, and listen. Another anecdote - my mom used to get so frustrated because she would ask me to do something and I'd say, "Yeah, uh-huh, sure," and then go right back to playing my video game or chatting with friends. Until I realized that what I needed was just a self-imposed time limit. So I had her ask, "The garbage needs to be taken out. When can you do that?"
By asking me when, it forced me to engage and make a decision. Sometimes I would say, "I can do it right now." Other times I would say, "Uh... I'll get it done by 3:30, I'm in the middle of this thing."
She listened to what I needed, and it made her life better because she didn't have to continually hound me, and it made my life better because she wasn't continually hounding me.