Find zero of a polynomial function

F(X)= 3x^3 - 5x^2 + 48x - 80

answer in the back of the book says 5/3, +/-4i, and (3x-5)(x-4i)(x+4i)

I keep trying but I cant get the right answer.

Please help me with detail! Thanks!

F(X)= 3x^3 - 5x^2 + 48x - 80
Use the "factor by grouping" technique:
3x^3+48x-5x^2-80=0
3x(x^2+16)-5(x^2+16)=0
(3x-5)(x^2+16)=0
3x=5
x=5/3
x^2+16=0
x^2=+/-16
x=+/-4i
(3x-5)(x-4i)(x+4i)