Something having to do with roots and i and stuff

$\large[(x-1)^2+4x][(x-1)^2+x][(x-1)^2+2x]=8x^3$

Suppose $a_i$ where $i={{1,2,3,4,5,6}}$ are the 6 complex roots of the equation above.

And $\arg(x_j)\leq \arg(x_k)$ for $j\leq k$ .

In which quadrant does $x_1x_6$ lie in?

Details and Assumptions :

• $0\leq \arg(x_i)<2\pi$

• You may want to use a calculator at the end after you had found the exact values of the roots.

All credit for this problem goes to Sean Ty.