Factorise:

$6\left(2 x-\frac{3}{x}\right)^{2}+7\left(2 x-\frac{3}{x}\right)-20=6\left(2 x-\frac{3}{x}\right)^{2}+15\left(2 x-\frac{3}{x}\right)-8\left(2 x-\frac{3}{x}\right)-20$

$=\left[3\left(2 x-\frac{3}{x}\right)\right]\left[2\left(2 x-\frac{3}{x}\right)+5\right]-4\left[2\left(2 x-\frac{3}{x}\right)+5\right]$

$=\left[2\left(2 x-\frac{3}{x}\right)+5\right]\left[3\left(2 x-\frac{3}{x}\right)-4\right]$

$=\left(4 x-\frac{6}{x}+5\right)\left(6 x-\frac{9}{x}-4\right)$

Hence, factorisation of $6\left(2 x-\frac{3}{x}\right)^{2}+7\left(2 x-\frac{3}{x}\right)-20$ is $\left(4 x-\frac{6}{x}+5\right)\left(6 x-\frac{9}{x}-4\right)$.