Question
$$8(x-3)+2(x-9)\cdot8(x-3)+2(x-9) = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 91 }{ 16 }-\dfrac{\sqrt{ 2041 }}{ 16 } & x_2 = \dfrac{ 91 }{ 16 }+\dfrac{\sqrt{ 2041 }}{ 16 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 8(x-3)+2(x-9)\cdot8(x-3)+2(x-9) &= 0&& \text{simplify left side} \\[1 em]8x-24+(2x-18)\cdot8(x-3)+2x-18 &= 0&& \\[1 em]8x-24+(16x-144)(x-3)+2x-18 &= 0&& \\[1 em]8x-24+16x^2-48x-144x+432+2x-18 &= 0&& \\[1 em]8x-24+16x^2-192x+432+2x-18 &= 0&& \\[1 em]16x^2-184x+408+2x-18 &= 0&& \\[1 em]16x^2-182x+390 &= 0&& \\[1 em] \end{aligned} $$
$ 16x^{2}-182x+390 = 0 $ is a quadratic equation.
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