Factorise: 6x^2-3x-3=0

Since the equation shows a 6x^2, we know that in the brackets we must have either: (2x+a)(3x+b) or (6x+a)(x+b) However we know the last two numbers must multiply to make -3, hence a and b must be +1 and -3 respectively and so we know the second solution is the one to use. This leads us to the final step --> the inner number must be the added product of the x terms and a and b. This means that to get -3x we need to place the numbers as follows: (6x+3)(x-1) This is because (6x)(-1)=-6x and (x)(3)=3x and so the sum of these numbers gives us the middle term.