Factorise 6x2+42x−48 completely.

Sure, here are the steps to factorise the given expression:

1. First, we can take out the common factor from the expression. The common factor in 6x^2 + 42x - 48 is 6. So, we get:

   6(x^2 + 7x - 8)

2. Now, we need to factorise the quadratic equation inside the brackets. We are looking for two numbers that multiply to -8 and add to 7. The numbers are 8 and -1. So, we get:

   6(x - 1)(x + 8)

So, the factorised form of 6x^2 + 42x - 48 is 6(x - 1)(x + 8).