$$4x^6+x^3+0 = x+2$$
Answer
$$ \begin{matrix}x_1 = -0.87498 & x_2 = 0.90288 & x_3 = 0.44807+0.87053i \\[1 em] x_4 = 0.44807-0.87053i & x_5 = -0.46202+0.66842i & x_6 = -0.46202-0.66842i \end{matrix} $$
Explanation
$$ \begin{aligned} 4x^6+x^3+0 &= x+2&& \text{move all terms to the left hand side } \\[1 em]4x^6+x^3+0-x-2 &= 0&& \text{simplify left side} \\[1 em]4x^6+x^3+0-x-2 &= 0&& \\[1 em]4x^6+x^3-x-2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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