$$107328\cdot(1-x^{8+1})-107328\cdot(1-x) = (1-x)\cdot927476$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = 1.01712 & x_3 = -1.41158 \\[1 em] x_4 = 0.81771+0.99207i & x_5 = 0.81771-0.99207i & x_6 = -1.02512+0.95371i \\[1 em] x_7 = -1.02512-0.95371i & x_8 = -0.09535+1.35956i & x_9 = -0.09535-1.35956i \end{matrix} $$
Explanation
$$ \begin{aligned} 107328\cdot(1-x^{8+1})-107328\cdot(1-x) &= (1-x)\cdot927476&& \text{simplify left and right hand side} \\[1 em]107328\cdot(1-x^9)-107328\cdot(1-x) &= 927476-927476x&& \\[1 em]107328-107328x^9-(107328-107328x) &= -927476x+927476&& \\[1 em]107328-107328x^9-107328+107328x &= -927476x+927476&& \\[1 em]107328-107328x^9-107328+107328x &= -927476x+927476&& \\[1 em]-107328x^9+107328x &= -927476x+927476&& \text{move all terms to the left hand side } \\[1 em]-107328x^9+107328x+927476x-927476 &= 0&& \text{simplify left side} \\[1 em]-107328x^9+1034804x-927476 &= 0&& \\[1 em] \end{aligned} $$
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