Answer
$-3i,-3,\frac{1}{2},4$
Work Step by Step
Step 1. Given a zero $x=3i$, we know another zero is $x=-3i$, thus $(x+3i)(x-3i)=x^2+9$ is a factor.
Step 2. Perform a division as shown in the figure to get the quotient $2x^3-3x^2-23x+12$ (one can also perform synthetic divisions to get the same result).
Step 3. Solve $2x^3-3x^2-23x+12=0$ graphically to get $x=-3,\frac{1}{2},4$ (one can also use synthetic division to find one more zero then solve the resulting quadratic.)
