Answer
$x=-2,\frac{1}{2}, 3$
Work Step by Step
Step 1. As $-2$ is a zero of $f(x)$, we can try to divide $f(x)$ by $x+2$
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{2,-3,-11,6\}$ and the divisor is $x+2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(2x^2-7x-3)(x+1)=(2x-1)(x-3)(x+2)$; thus we can find the zeros of $f(x)$ as $x=-2,\frac{1}{2}, 3$
