Work out the solutions to the following quadratic equation: x² + 7x + 10 = 0 by factorising.

Firstly, we have to factorise the quadratic equation. So what this involves is finding two numbers which add up to 7 but also multiply to give 10 at the same time. To help you with this we can find common multiples of 10, so that would include 10 and 1, 2 and 5. Now we can see that 10 and 1 cannot add or subtract to make 7 so it has to be 5 and 2.
So what we can now put these into double brackets: (x+5)(x+2) = 0. Next we need to find a value for x so that when these brackets are multiplied together it equals to 0. This means that either (x+5)=0 or (x+2)=0. This leaves you with 2 solutions: x=-5 or x=-2. You can double check these answers by substituting these values back into the original quadratic equation and it should equal to 0 for both values.