Howdy y'all.

I'm a full-time employee making around $55k a year. My employer takes out all my taxes.
I'm going to start a second, part-time job soon with another company as an independent contractor. (Making $21K a year)
I read somewhere online that I could just increase the withholding at my full-time job so that I wouldn't have to pay taxes quarterly.
It didn't give any other information... for instance, how much more should I have withheld per paycheck?
Has anyone else heard of this and know that it can be done?
Any help is much appreciated!