Factorise x^2-x-6=0, and solve, finding the values of x

When you factorise an equation, the final form should look like this: (x+a)(a+b)=0 in order to work out the possible value(s) for x. As a result, working backwards, we expand the already factorised final form into x^2+ax+bx+ab=0. As this is a generalised form, we can use this to work out the factorised form of x^2-x-6=0. Therefore, ab has to equal -6. Consequently, ax+bx=-1x. This tells us that a+b=-1. We now have to different equations that can help us to work out what the values of a and b are, as the values of a and b need to give -6 when multiplied together, as well as give the answer of -1 when added together. Going through the possible values that a/b may have, we find that -3 and 2 work, as (-3)(2)=-6, and (-3)+(2)=-1. This, therefore, gives us the answer to the first part of the question. The factorised form of x^2-x-6=0 is (x-3)(x+2)=0. To answer the next part of the question, we use this factorised form. We know that anything multiplied by 0 gives the answer 0. Therefore, as the result of this equation is given to equal to 0, we know that either x-3, or x+2, have to give the value of 0. We can now make two separate equations, x-3=0, and x+2=0. This gives us the values of x to be 3, and -2, and hence we have solved the problem.