Factorize:

We have:

$6 \sqrt{3} x^{2}-47 x+5 \sqrt{3}$

Now, we have to split $(-47)$ into two numbers such that their sum is $(-47)$ and their product is 90 .

Clearly, $(-45)+(-2)=-47$ and $(-45) \times(-2)=90$

$\therefore 6 \sqrt{3} x^{2}-47 x+5 \sqrt{3}=6 \sqrt{3} x^{2}-2 x-45 x+5 \sqrt{3}$

$=2 x(3 \sqrt{3} x-1)-5 \sqrt{3}(3 \sqrt{3} x-1)$

$=(3 \sqrt{3} x-1)(2 x-5 \sqrt{3})$