Give the possible values of x when 2x^2-x-6=0

first of all the equation needs to be written in the form (ax+b)(x+c) 

because 2 can only be made by multiplying 2 and 1 we know that a=2 so (2x+b)(x+c)

-6 can be made by multiplying 2 and -3, -2 and 3, -6 and 1 or 6 and -1

the easiest way to work this out is trial and error to make sure we can get -x in the middle

so from this we can write it as (2x+3)(x-2)=0

because 0 multiplied by anything =0 we know that the contents of each bracket can =0: 2x+3=0 and x-2=0

by rearranging these equations to solve for x we can work out that the answer to this question is x=2 or x=-3/2