Why are my subwoofers making a solid base line?

I just installed two 12' pioneer subs in my 2014 honda accord. The subs are working off of the back two speakers. I have the remote cable folded over the accessory fuse so the amp turns on and off when I turn the car on. Whenever I have all the doors closed and the radio is on the subs produce a solid bass line while a song is playing but whenever I press the gas pedal or open one of the doors the bass line stops.

You're running into the active noise control feature on the Accord. The system uses the rear speakers to play an out-of-phase noise signal to cancel out background noise in the vehicle. Since the subwoofer gets its input signal from the rear speakers, it's playing back the ANC signal.

There should be a microphone mounted up in the headliner above the rear window; disconnecting the mike will disable the ANC function.

Visit a Honda owner's forum and search for ANC and you should find posts from people who had the same issue.