Solve \[ a^{2 x}\left(a^{2}+1\right)=\left(a^{3 x}+a^{x}\right) a . \]

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Solve
\[
a^{2 x}\left(a^{2}+1\right)=\left(a^{3 x}+a^{x}\right) a .
\]
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