I found a quick way of factorising quadratics with a coeficient of x that is greater than one. For example:

6x2+19X+10

[list=1][*] Find two numbers which multiply together to give the product of the constant (10) and the coeficient of x2 (6) and add together to give the coeficient of x.

In this case the product of the constant and the coeficient of x2 is:
60

And two numbers which add together to give the coeficient of x and multiply together to give 60 are:

4 and 15
[*] Rewirte the equation with the x coefitients split :
6x2+4x+15x+10
[*]Now take the commmon factors out and rewrite as:

3x(2x+5) +2(2x+5)
[*] The two factors can now be extracted visually. The answer is correct if both the factors in brackets match, in this case (2x+5) which is also a factor. The other factor can now be extracted and is (3x+2) - its split among the 2 lots of (2x+5)'s.[/list=1]

Solved completely this gives x a value of -5/2 and -2/3.

I'm yet to find a quick way of solving quadratics with an x2 coeficient that is less than 0 e.g. -5 of something. So if anyone know of a way I'd be interested to know.