$$157203\cdot(1-x^{9+1})-157203\cdot(1-x) = (1-x)\cdot1088122$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = 0.94697 & x_3 = -0.70564+1.10783i \\[1 em] x_4 = -0.70564-1.10783i & x_5 = -1.25562+0.43621i & x_6 = -1.25562-0.43621i \\[1 em] x_7 = 0.85463+0.85845i & x_8 = 0.85463-0.85845i & x_9 = 0.13313+1.27142i \\[1 em] x_10 = 0.13313-1.27142i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 157203\cdot(1-x^{9+1})-157203\cdot(1-x) &= (1-x)\cdot1088122&& \text{simplify left and right hand side} \\[1 em]157203\cdot(1-x^{10})-157203\cdot(1-x) &= 1088122-1088122x&& \\[1 em]157203-157203x^{10}-(157203-157203x) &= -1088122x+1088122&& \\[1 em]157203-157203x^{10}-157203+157203x &= -1088122x+1088122&& \\[1 em]157203-157203x^{10}-157203+157203x &= -1088122x+1088122&& \\[1 em]-157203x^{10}+157203x &= -1088122x+1088122&& \text{move all terms to the left hand side } \\[1 em]-157203x^{10}+157203x+1088122x-1088122 &= 0&& \text{simplify left side} \\[1 em]-157203x^{10}+1245325x-1088122 &= 0&& \\[1 em] \end{aligned} $$
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