$$107328\cdot(1-x^{8+1})-107328\cdot(1-x) = (1-x)\cdot937254$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -1.41324 & x_3 = 1.01944 \\[1 em] x_4 = 0.81868+0.99323i & x_5 = 0.81868-0.99323i & x_6 = -1.02632+0.95483i \\[1 em] x_7 = -1.02632-0.95483i & x_8 = -0.09546+1.36115i & x_9 = -0.09546-1.36115i \end{matrix} $$
Explanation
$$ \begin{aligned} 107328\cdot(1-x^{8+1})-107328\cdot(1-x) &= (1-x)\cdot937254&& \text{simplify left and right hand side} \\[1 em]107328\cdot(1-x^9)-107328\cdot(1-x) &= 937254-937254x&& \\[1 em]107328-107328x^9-(107328-107328x) &= -937254x+937254&& \\[1 em]107328-107328x^9-107328+107328x &= -937254x+937254&& \\[1 em]107328-107328x^9-107328+107328x &= -937254x+937254&& \\[1 em]-107328x^9+107328x &= -937254x+937254&& \text{move all terms to the left hand side } \\[1 em]-107328x^9+107328x+937254x-937254 &= 0&& \text{simplify left side} \\[1 em]-107328x^9+1044582x-937254 &= 0&& \\[1 em] \end{aligned} $$
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