Factor and find all the zeros of 2x^3+3x^2-8x+3 if - 3 is a zero

Using synthetic division, you can find the quadratic factor to be

... 2x^2 - 3x + 1

That, in turn, factors as

... (2x - 1) (x - 1)

So the complete factorization is

... (2x - 1) (x - 1) (x + 3)

and the zeros are confirmed by a graphing calculator to be

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