S.O.S. Mathematics CyberBoard

I'm having a hard time solving this problem in a reasonable manner that doesn't involve a page full of algebraic equations...

I have:
A=[0,1,-2;3,-2,1;2,-4,-5] and b = [2;0;1]

I have to determine the column vector g so that the eigenvalues of Ac=A-bgT (g transpose) are:

-3, -2±3.674i

when calculating Ac=A-bgT I get A- [2;0;1]*[g1;g2;g3]=
[0,1,-2;3,-2,1;2,-4,-5] - [2g1,2g2,2g3;0,0,0;g1,g2,g3]
=[-2g1,1-2g2,-2-2g3;3,-2,1;2-g1,-4-g1,-5-g3]

the calculations get pretty lenghty here...I have entered the information into MATlab and the closes values I can get for g are g=[0.5;1.5;-1] but it doesn't give me the exact eigenvalues.

is there an easier way to do this?? any help would be appreciated, thanks!!

You know the matrix's characteristic polynomial so...

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yes...it's about 6 lines long. my approach is to substitute the 3 eigenvalues for lambda to get three equations. will somehow solving these equations for the 3 unknowns give me the correct answers?

i have tried solving this series of three equations for the three unknowns in MATlab and it returns 2 values for each unknown. neither of these values return the correct eigenvalues when i calculate them. where am i going wrong?