How do you solve quadratic inequalities?

Quadratic inequalities generally don't arrive in the standard quadratic form (Ax^2 + Bx +c) and so can be sometimes difficult to spot. However, if you see an X^2 - or brackets that expand to X^2 - on either side of the equation, then you can recognize that it will form a quadratic. GCSE maths only requires you to deal with quadratics, so if you see an X^3 then re-read the question and double check your expansion - you've either made a mistake or you're not expected to solve it. 

Expand out all brackets, and move everything onto one side so you have an equation that is greater or less than 0. You do not have to change the sign - you're just adding/ taking away. Now solve the quadratic just like you would normally. You can look at a number of marks the question gives you as an indication as to whether you should expect it to factorise easily.  Remember: quadratic solutions will give you the values that make it equal to 0, so you know these are the points where the line crosses over. Write out these values and test numbers between them. For example, if your answers are 3 and 1 - test 2. If you are looking for values for which your equation is greater than 0, and your test for 2 is positive then you know that the positive range must be greater than 1 and less than 3. Remember - you just write less than/greater than - it cannot be equal! If you want, you can check on a graph.