Is It Possible to Solve This Corrected Quartic Polynomial Equation?

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\[x^4+16x-12=0\]

\[x^{4}-12+16+16x-16=0\]

\[x^{4}+4x^{2}+4-4x^{2}+16x-16=0\]

\[(x^{2}+2)^{2}-(2x-4)^{2}=0\]

\[(x^{2}-2x+10)(x^{2}+2x-2)=0\]
 
Nice solution! There is a typo for the first factor: it should be $x^2-2x+6$
 

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