Help me factorize a quadratic equation in a complex variable

The equation is: (appears while solving a trigonometric integral using residue theorem)



2Z²+iZ²-6Z+2-i

=(2+i)Z²-6Z+(2-i)



The roots are:

Z₁=(2-i) and Z₂=(2-i)/5



I can't write the equation in factored form.

If I simply write it like this:

{z-(2-i)}{5z-(2-i)}

It doesn't give the same equation back i.e.

{z-(2-i)}{5z-(2-i)}=5Z²-12Z+6iZ+3-4i

which is not the equation that I started with.



Can anyone please write the equation in factored form...