Does it violate the GPL v3 if I were to use a gpl licensed firmware with my closed-source hardware that I am selling? Or do both have to be open-source, or do I just have to make the firmware source freely available?
There are lots of cases of consumer devices using GPL'd firmware. TiVo was the big name one because certain people were annoyed that even though TiVo released their changes, you couldn't take that and make your own changes and put it on your TiVo because they locked their boxes. In fact that's what caused the "TiVo'isation" clause in the next version of the GPL (v3).
However, even GPLv3 doesn't require that the hardware be open source (to the best of my knowledge, IANAL). The GPLv3 seems to say that if you pulled a TiVo then you'd have to release the software changes you made and provide instructions/tools to allow people to replace the firmware on the device with new firmware that they create with their own changes.
Pretty much any CPU out there isn't open source, so how could vendors sell any hardware that had GPL software on it?
That said, you should thoroughly read the license before using it. I have read it, and I don't recall anything about requiring the hardware to be open source.