Question 59580
6x^2 - 42x + 72
 To factorise this, we need to find 2 numbers whose sum is -42 and whose product = 6*72 = 432

We find the numbers to be - 18 and - 24

Now 6x^2 - 42x + 72 
= 6x^2 - 18x - 24x + 72  [splitting the middle term]
= 6x(x - 3) - 24(x - 3)  [Removing the common factor]
= (x - 3) (6x - 24)
= (x - 3) (6) (x - 4)  [Removing the common factor]

So 6x^2 - 42x + 72  = 6(x - 3)(x - 4)

To find the roots, we equate this to zero.
==>  6(x - 3)(x - 4) = 0
==>  x - 3 = 0    or x - 4 = 0
==>  x = 3  or  x = 4

So 3 and 4 are the roots of the given equation.