Answer
$-\frac{1}{2},1,\frac{-1\pm i}{2}$
Work Step by Step
1. List possible rational zeros as $\pm1,\pm1/2,\pm1/4$
2. Test these values using synthetic division to find two zeros $-1/2,1$
3. $P=(2x+1)(x-1)(2x^2+2x+1)$
4. Zeros $-\frac{1}{2},1,\frac{-1\pm i}{2}$