How do I start this?

I need to find the area between these two curves, but the equations are confusing the heck out of me on trying to find the intercepts:

y=e^x - 2 and y= -3x^3 -2x^2 +4x

I set them equal to each other: e^x - 2= -3x^3 -2x^2 +4x ----> 0= -3x^3 -2x^2 +4x -e^x +2 , but then it occurred to me how would this even factor? It might just be the e^x that's confusing me. When I graph it on my calculator, I can see them. By hand how would I get the intercepts? Thanks for any and all help

Are you sure you have posted the exact problem?

As far as I can see, these two functions intersect at one point (x = 0.180075) only (-2<x<10).

You possibly cannot find area between curves - unless those are bounded.
 
oh geez I'm sorry. They are bounded by that region of those two equations. Sorry :( I updated the question so it reads correct. I also had the wrong number in there too. Just went way too fast. Sorry.
 
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