[Precalculus] Finding the Zeros of a Function

[Pathos]

Given the polynomial and a zero, find the other zeros.

g(x) = 4x^3 + 23x^2 + 34x - 10

Given Zero: -3 + i

I am stuck on this problem. I know if -3 + i is zero, then
(x - (-3 + i)) and (x - (-3 - i)) are factors. I multiplied those together to get x^2 + 6x + 1. I used long division to divide the original function by x^2 + 6x + 1, but that did not help.

I also made a rational zero list and did synthetic division with the hope of finding a zero, but I could not find a zero by that method too. Could someone help me?

EDIT: Please disregard this thread. I made an error when using synthetic division with 1/4 as the possible zero. Thus, 1/4 is the other zero along with the two mentioned above. >_<