Answer
$x=-4, -\frac{1}{3}, 2$
Work Step by Step
Step 1. As $-\frac{1}{3}$ is a zero of $f(x)$, we can try to divide $f(x)$ by $x+\frac{1}{3}$
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{3,7,-22,-8\}$ and the divisor is $x+\frac{1}{3}$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(3x^2+6x-24)(x+\frac{1}{3})=3(x^2+2x-8)(x+\frac{1}{3})=3(x+4)(x-2)(x+\frac{1}{3})$; thus we can find the zeros of $f(x)$ as $x=-4, -\frac{1}{3}, 2$
