I am driving going 35 miles per hour and I press the break pedal the car shakes.

Have an experienced *auto mechanic* test drive your car, one that's been doing it for a good while! .. Ol Joe or George down the street in the independent repair shop probably your best bet.. Got to be excessive runout in brake rotors//drums or both... Good luck.

If you schedule a diagnostic service with Wrench, we'll come to you for free and tell you what's wrong. We then can order the right parts and come back and fix it for you at your home. We're usually cheaper than independent shops and a dealer and certainly more convenient. www.getwrench.com