$$12n^5+6n-2-(9n-13n^5-13) = 0$$
Answer
$$ \begin{matrix}n_1 = -0.88612 & n_2 = 0.675+0.45965i & n_3 = 0.675-0.45965i \\[1 em] n_4 = -0.23194+0.83112i & n_5 = -0.23194-0.83112i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 12n^5+6n-2-(9n-13n^5-13) &= 0&& \text{simplify left side} \\[1 em]12n^5+6n-2-9n+13n^5+13 &= 0&& \\[1 em]25n^5-3n+11 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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