How would one start this factorisation?

$\displaystyle P(z) = z^2 +(3 +2i)z +6i$

Would you just sub in values of z until you get P(z) to equal zero? Or is there a better way to approach this problem?

I subbed in values til P(z) equals zero and I found -3 to be a root, but is there a more sophisticated way to solving this problem than just subbing in values until you get a zero?

David.