$$14x^{16}+21x^{11}+7 \cdot \frac{x^6}{7}x^2 = 0$$

$$ \begin{matrix}x_1 = 0 & x_2 = -0.65511 & x_3 = -1.07831 \\[1 em] x_4 = 0.14525+0.62474i & x_5 = 0.14525-0.62474i & x_6 = -0.40734+0.5004i \\[1 em] x_7 = -0.40734-0.5004i & x_8 = 0.58959+0.27708i & x_9 = 0.58959-0.27708i \\[1 em] x_10 = 0.87273+0.64115i & x_11 = 0.87273-0.64115i & x_12 = -0.33352+1.0368i \\[1 em] x_13 = -0.33352-1.0368i & \\[1 em] \end{matrix} $$

In order to solve $ \color{blue}{ 98x^{16}+147x^{11}+7x^{4} = 0 } $, first we need to factor our $ x^4 $.

$$ 98x^{16}+147x^{11}+7x^{4} = x^4 \left( 98x^{12}+147x^{7}+7 \right) $$

$ x = 0 $ is a root of multiplicity $ 4 $.

The remaining roots can be found by solving equation $ 98x^{12}+147x^{7}+7 = 0$.

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using Newton method.

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