Here is an alternate approach.
Imaginary roots occur in pairs, so x = 2i, and x = -2i are roots as well as x = -3.
We can write factors in the form (x - (-3)) (x + 2i) (x - 2i) = 0
Multiply the factors in parentheses. (x + 3) ( x2 - 4i2) = 0
Expand further to get x3 - 4i2x +3x2 - 12i2 = 0
This simplifies to x3 + 3x2 +4x +12 = 0
Prove by inserting the given roots for x which should give zero.