Asymptote and end behaviour

Given the rational function 2x^2-8x+5/2x63-5x^2+3x. Determine the following (show all work, explaining how/why that is the result):

a)horizontal and vertical asymptote(s)

b)end behaviours....provide a sketch of the function when the above steps have been completed.

Here's what I have so far...

__2x^2-8x+5__

2x^3-5x^2+3x

= __3-8/x+5/x^2__

2/x-5+3/x

HA= __-3__

5

2x^3-5x^2+3x=0

x=0, x=3/2,x=1...

I'm not sure what I have so far is right. Please help me continue to find the VA...and the end behaviour. Thank you!