Factorise the equation x^2 +5x = 6

On first glance, this looks like it is going to be a quadratic equation, so let’s try and put it in the form ax² + bx + c = 0 which we can factorize. If we subtract 6 from each side, we end up with x² +5x - 6 = 0, which is exactly what we need. Now, to factorize this quadratic, we can use one of three main tools – factorizing by observation, completing the square and the quadratic formula. Let’s start with factorizing, and if this is not possible we can move on I think the best thing to do first is to write out all the factors of -6, as two numbers must multiply to make -6 and add to make 5 if we are going to be able to use factorization by observation. Our multiple pairs are (-1 and 6), (1 and -6), (2 and -3), and (-2 and 3). If we look at these pairs, we can see that adding -1 and 6 gives us 5 as required, therefore we can factorize this quadratic to (x-1)(x+6) = 0. We can expand this out again fully to check we have done this correctly.