Find x when 2x^2 −x−6=0

The equation is: 2x^2 - x -6 =0

step 1. (2x) and (x)  now you need to separate out this equation into two further brackets. You start with the highest power of X, in this case 2X^2. As 2 has no smaller factors, you can separate this into (2X) and (X). To ensure you have done this correctly, multiply out your brackets to double check that they come to 2X2.

step 2. You now have '2x' and 'x'. 

You need to find two different values of X that 

1. add up to -1

2. multiple to five -6

the only factors of 6 are: 1 and 6, and 2 and 3. 

To try them both, substitute them:

(2x+6)(x-1)

 > 2x^2 -2x+6x -6 

> 2x^2 +4x -6

this clearly does not work, so try and substitute 3 and 2. 

(2x+3) (x-2)

> 2X^2 -4X +3X +6

>2X^2 -X +6

therefore the answer to the solution is simply:

(2X+3) (X-2)