$$ \begin{aligned} (n-1)(2n-2) &= 0&& \text{simplify left side} \\[1 em]2n^2-2n-2n+2 &= 0&& \\[1 em]2n^2-4n+2 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-4x+2 = 0 $ is a quadratic equation.
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