Polynomial expression with modulo

Question

$1 + x + x^2 + x^3 + x^4 + x^5 + x^6 = 0 \pmod{29}$

I converted the expression into $(1-x^7) / (1-x)$ But I couldn't find the roots.

Answer 1

I got $$x^6+x^5+x^4+x^3+x^2+x+1=(x-7)(x+13)(x+9)(x+6)(x+5)(x+4).$$