$$-64x^6+112x^4-56x^2+7 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.43388 & x_2 = -0.43388 & x_3 = -0.78183 \\[1 em] x_4 = 0.78183 & x_5 = -0.97493 & x_6 = 0.97493 \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver