Question

how to factor 3x^2-3x+9/16

Answer 1

I would factor out 3/16 to get

(3/16)(48x^2 - 16x + 3)
the trinomial does not factor

If you meant:
(3x^2 - 3x + 9)/16
then
= (3/16)(x^2 - x + 3)
again the trinomial does not factor, but notice how important brackets become ?