Answer
$\frac{5\pm \sqrt {37}}{6}$
Work Step by Step
Use the Remainder and Factor Theorem:
$P(-2)=3\times16+8\times8-14\times4-31\times2+6=0$
$P(3)=3\times81-8\times27-14\times9+31\times3+6=0$
This proves that $-2,3$ are zeros of P.
Use synthetic division to reduce P to quadratic form as
$P(x)=(x+2)(x-3)(3x^2-5x-1)$ and the other two zeros are
$x=\frac{5\pm \sqrt {37}}{6}$