4n²-4n-3=(2n-3)(2n+1).
But 4n²-4n+3 factorises into complex factors only so there are no real solutions.
In case you were expecting complex factors, here is the solution:
4n²-4n+3=4(n²-n+¾)=
4(n²-n+¼-¼+¾)=
4((n-½)²+½)=
4(n-½+i/√2)(n-½-i/√2), where i=√-1.
This can be written:
(2n-1+i√2)(2n-1-i√2).