Triangles, Edgeflow, Sphere

I’ve been working on getting better at manual retopology/topology with vanilla Blender. I just want to get a solid handle on the principles and theory of it all. And there’s one very fundamental aspect in particular that I can’t seem to get a good handle on.

In the image is a 32-vertex UV sphere that I sliced at a particular angle with a knife to produce this shape. Once I got rid of the unnecessary leftover vertices. I beveled the edge and turned my attention to the edgeflow. This is where I got stuck. Sometimes, I get through this and everything turns out great. Other times, I run into an issue like the one here and I’m unsure on how to deal with it. My goal is to understand topology and edgeflow well enough so that I ALWAYS know what to do about it.

In this image, my issue is the triangles that pop up along edge where I put the bevel. I want all quads for this mesh. How do I go about redirecting the edgeflow so that I can get rid of the 4 triangles. Please keep in mind, I don’t just want a solution for this image. I’m trying to resolve my thinking on this so that I can handle ANY topology cleanup situation without getting stuck. In other words, I’m looking to understand and internalize the thinking, the theory, the guidelines that I can apply to ALL topology challenges going forward.

I’ve done about 25 hard surface tutotials in the past month, but watching and following along is VERY different from building a foundation to build your own expertise with this.

The first image is the problem. The 2nd image is the solution I thought of while ryping this note (adding a loopcut that extends from the subdivided base of the triangle. The third image shows another angle. Please note that this solution I came up with brought some shading errors with it, so its not perfect.

Now, get this: The bottom image shows the solution I came up with after an hour of noodling yesterday. I don’t remember how I did it. That’s the issue. I started modeling the same shape today, same dimensions, and I couldn’t arrive at this smooth edgeflow solution.

PLEASE HELP!