$$8x^2+2x-1=0$$
You need to find 2 numbers that multiply to give 8*-1=-8
They mult to give a neg so one is pos and the other is neg.
And they have to add to +2 So the biggest one will be the positive one.
The numbers are +4 and -2
Now you are going to split 2x up into 4x-2x so the equation becomes
$$8x^2+4x-2x-1=0$$
Now you can factorise the pairs like this
$$4x(2x+1)-1(2x+1)=0$$
Now factorise the LHS properly
$$(4x-1)(2x+1)=0\\
so\\
4x-1=0\qquad or \qquad 2x+1=0\\
4x=1\qquad \qquad or \qquad 2x=-1\\
x=1/4\quad \qquad or \qquad x=-1/2\\$$
OR
You could just use the quadratic formula.
Other helpful threads:
http://web2.0calc.com/questions/grouping-method-and-factorizing-quadratic-equations
http://web2.0calc.com/questions/factorising-any-quadratic-formula-some-thoughts
http://web2.0calc.com/questions/quadratic-formula-do-you-have-trouble-remembering-it