Factor complex equation

Question

Im having some difficulty in factoring the following complex equation. The image bellow is taken from WolframAlpha, can anyone explain how I can factor this equation.

In the task I am told one solution has a real part of 1.

Answer 1

$z^4-2z^3+12z^2-14z+35=0$

Rewrite the term $12z^2$ as $5z^2+7z^2$:

$z^4-2z^3+5z^2+7z^2-14z+35=0$

Take out the common factors:

$z^2(z^2-2z+5)+7(z^2-2z+5)=0$

Factored form:

$(z^2+7)(z^2-2z+5)=0$

The solutions to this equation are:

$x=\pm\sqrt{7}i$ and $x=1\pm2i$.