Answer
$x=-\frac{3}{2}, -\frac{1}{3}, \frac{1}{2}$
Work Step by Step
Step 1. As $-\frac{3}{2}$ is a zero of $f(x)$, we can try to divide $f(x)$ by $x+\frac{3}{2}$
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{12,16,-5,-3\}$ and the divisor is $x+\frac{3}{2}$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(12x^2-2x-2)(x+\frac{3}{2})=2(6x^2-x-1)(x+\frac{3}{2})=2(3x+1)(2x-1)(x+\frac{3}{2})$; thus we can find the zeros of $f(x)$ as $x=-\frac{3}{2}, -\frac{1}{3}, \frac{1}{2}$
