Question
$$(4x^{10}+9x^7)(-4x^{10}-9x^7) = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} (4x^{10}+9x^7)(-4x^{10}-9x^7) &= 0&& \text{simplify left side} \\[1 em]-16x^{20}-36x^{17}-36x^{17}-81x^{14} &= 0&& \\[1 em]-16x^{20}-72x^{17}-81x^{14} &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -16x^{20}-72x^{17}-81x^{14} = 0 } $, first we need to factor our $ x^14 $.
$$ -16x^{20}-72x^{17}-81x^{14} = x^14 \left( -16x^{6}-72x^{3}-81 \right) $$$ x = 0 $ is a root of multiplicity $ 14 $.
The remaining roots can be found by solving equation $ -16x^{6}-72x^{3}-81 = 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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