Asymptotes of (x-4) (x+3)

Vertical asymptotes of an expression occur at the excluded values of a function. Assuming you mean that (x-4) (x-3) is the denominator, then you would find the 'solutions.'

x - 4 = 0, x = 4

x + 3 = 0, x = - 3

Therefore, your vertical asymptotes occur at x = 4, - 3.