I applaud your effort to describe why we factor equations, I just don't think you've done that here. A high-level question needs a high-level answer before

I applaud your effort to describe why we factor equations, I just don't think you've done that here. A high-level question needs a high-level answer before diving in. I'm not a fan of "Because that's where the graph touches the x-axis" because it again leads to... Why does touching the x-axis matter? Because that's where the the system "becomes what you want it to become", i.e, where: x^2 + x - 6 = 0 x^2 + x = 6 You're trying to describe factoring to someone without the basic fundamentals to even need to do factoring. By analogy, that's like saying "I want to explain why we need piston rods, but I don't want to mention anything about engines." Prerequisites are meaningful. [Edit] I just verified that graphing is typically taught after factoring, so I at least sympathize with the challenge you're facing.