The normal to the curve \( 5 x^{5}-10 x^{3}+x+2 y+6=0 \) at the poi...

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The normal to the curve \( 5 x^{5}-10 x^{3}+x+2 y+6=0 \) at the point \( P(0,-3) \) is tangent to the curve at some other point(s). Find those point(s)?
\( \mathrm{P} \)
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