Factorise:

The given expression is $4 n^{2}-8 n+3$.

Find two numbers that follow the conditions given below:

Sum $=-8$

Product $=4 \times 3=12$

Clearly, the numbers are $-6$ and $-2$.

$4 n^{2}-8 n+3=4 n^{2}-2 n-6 n+3$

$=2 n(2 n-1)-3(2 n-1)$

$=(2 n-1)(2 n-3)$