How do you factorise a quadratic equation

Factorising a quadratic can seem daunting at first but when broken down if to multiple steps it can be much more manageable. These steps will work for all basic quadratics so if you stick to the formula you will have no problem.
Lets look at an example X² + 2x + 3 = 6. The first step is to always put all the numbers your dealing with on one side. So by taking 6 away from both sides we end up with x² + 2x - 3 = 0. Now everything is on one side of the equation we begin to factorise it. Because of the x² Being the highest power we know we need 2 brackets each with an X at the start and because there is only 1x² We only need to 1 x at the start of each equation. Becuase the 2x has a + in-front of it and the 3 has a - in-front the number in the brackets must multiply to make a negative and add together to make a positive, so we know there is a negative and positive. Our equation so far is (x + ?)(x - ?). We have dealt with x² and now need to deal with the 2x-3 part of the equation. The numbers we choose must add up to make 2 and multiply together to make - 3. This is the tricky part since there real method to find these number out, you just have to think until they come to mind. In this case the numbers are + 3 and - 1 because 3x-x= 2x and 3*-1= -3. Our final formula is (x+3)(x-1)=0.
To summarise our steps are move all the components to one side, work out how many brackets are needed, work out how many xs are needed and finally work out what number need to complete the equation.


I have assumed the student has previous knowledge on quadratics and have made some unexplained links that some student would not understand. If I needed to I would be capable and happy to explain these to the students. I have also given a very basic explanation which doesn't go into full detail of factorising quadratics because the topic is so broad and complicated that I think it would need more time to fully explain how to use them but this is just a starter.