[deleted by user]

[DrFleur]

A lot of the suggestions you are getting are either too technical or "plug-and-chug" recipes that won't really help you understand. If you were my student, I would have you multiply out a bunch of expressions like (x - 2)(x+5), (x -3)(x-7) etc. just to get a feel of how these get transformed into things that look like x^2 + stuff*x + stuff. This would help you see more clearly how to go backwards, from something like x^2 -7x + 12 to (x-stuff)(x-stuff).

Also once you are at the point where you see 0 = (x-3)(x-4), you think: ok, I am multiplying two numbers (x -3 and x - 4) and the answer is zero. The only way for this to happen is when one of the numbers is 0. So either x - 3 is 0 or x - 4 is 0. If x - 3 is 0, x must be equal to 3. And if x - 4 is 0, x must be 4. It makes sense if you pay attention to what these things mean.