There's an error in P(x). It should be P(x)=x6-2x5-13x4+70x3-160x2+184x-80.
The zeroes are 2 (twice), 1, -5. By progressively dividing by these zeroes using synthetic division we can reduce P(x) to a quadratic:
1 | 1 -2 -13 70 -160 184 -80
1 1 -1 -14 56 -104 | 80
2 | 1 -1 -14 56 -104 80 | 0
1 2 2 -24 64 | -80
2 | 1 1 -12 32 -40 | 0
1 2 6 -12 | 40
-5 | 1 3 -6 20 | 0
1 -5 10 |-20
1 -2 4 | 0 = x2-2x+4.
x2-2x=-4,
x2-2x+1=-3,
(x-1)2=-3,
x=1±i√3 are the remaining two zeroes: 1+i√3 and 1-i√3.