The equations $\displaystyle 2x^3-2x^2$ and $\displaystyle -6x^2+30x$ produces intersection points at 0,0 and 3,36.

If I set them equal to each other and then solve for 0, I get the equation $\displaystyle 2x^3 + 4x^2 - 30x$ produces zeroes at 0 and 3.

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?