Is there a way to automatically remove ngons? As you can see, I am trying to make a computer screen, but am wondering how I can make my mesh of a screen correctly connect to the main frame. Do I have to manually use the knife tool? Or is there a better option? Thanks for all advice or suggestions!

The first picture is the subdivision gone wrong.
The second picture shows my original mesh.
From left to right:


Add loopcuts CTRL+R. Number of loopcuts = number of vertices (I marked them with blue dots) except those in the corners, because they already have a proper connection.
Select and delete Ngons: Delete->Faces. Select edges
Press W-> Edge Bridge Loops