You just apply Ruffini with the root you have. You end up with
Help would be greatly appreciated... z3 + (1 - 4i)z2 + (17 - 16i)z + (-87 - 116i) = 0, where z = 3 + 4i is one of the roots...
step by step working would be fandabadosy too; I know it's pretty basic but I've gone COMPLETELY blank
This is not a homework service
You can find the exact answer on the web.
To do it for yourself, divide the polynomial by to reduce it to a quadratic that you can solve.