Question 976041
What is that method?  The polynomial looks like might be a square expression, but hard to know just by looking.


{{{(2x^2+3)(2x^2+3)=4x^4+6x^2+6x^2+9}}}-----that's not it;


{{{(2x^2+1)(2x^2+3)}}}
...{{{2x^2+6x^2}}}...
...{{{8x^2}}}...
That is not it either.


{{{(4x^2+3)(x^2+1)=4x^4+3x^2+4x^2+3}}}------does not give what you want.


Jumping right to general solution method for "quadratic",
discrim is {{{9-4*4*9<0}}}, so no real solution for the {{{x^2}}}.


A quick check of the graph for {{{y=4x^4+3x^2+9}}} using software shows no roots, or no real roots.  Your left side member IS NOT factorable for real numbers.