what you stated are not equations. there has to be an equal sign for something to be an equation.

there is also a zero at -5If I set them equal to each other and then solve for 0, I get the equation produces zeroes at 0 and 3.

moreover, this is exactly the method used to find the points of intersection. why would you expect to get a different answer?

finding the solutions to is the same as finding the zeros of the function , since you are working with exactly the SAME equation. in the latter case you are solving for , which is the same as finding the solutions to the first equation.So, the x's from the intersection points and the x's from the zeroes are the same. Why? The graphs look completely different, what causes them to produce the same results?

as for the graphs, i think you are confusing them. the graphs of the 3 expressions will of course be different. and are two different graphs. the latter graph is also different, as it represents something else. its relation to the previous two graphs is that its zeros give the points of intersection of the two graphs