How do I factorise a quadratic equation?

A quadratic equation is one with a squared term, like 3x² + 9x. If you're asked to factorise an equation like this, you need to find the highest common factor. This means that you need to find the highest number that all the terms in your equation can be divided by and still give a whole number result.
For 3x² + 9x, this number is 3.
Dividing the equation by 3 gives us: x² + 3x.
Both terms also contain the variable x, the highest common factor of x²  and x is x.
Diving our new equation by x gives us: x+3.
If we multiply x+3 by 3 and by x we will get our original equation 3x² + 9x.
We can write this as 3x(x+3), and this is our answer.

You can check your result by multiplying out the brackets:
3xx= 3x²
3x3= 9x
And so, 3x(x=3)= 3x² + 9x.