How do you factorize a quadratic equation which has a coefficient of x^2 other than 1?

Factorise 6x² + x - 2 = 0

1. Firstly, multiply the coefficient of x² by the last number:

6 x -2 = -12

2. List all the factors of 12 and see which pair adds/subtracts to make 1:

Factors of 12: [1,12] [2,6] [3,4]    -----------> +4 - 3 = 1

3. Rewrite the quadratic equation, but split the x up into the above factors:

6x² + 4x - 3x - 2 = 0

4. Split the equation in half: 

(i) 6x² + 4x                  (ii) -3x - 2

5. Factorise both halves (hint: both brackets should be the same):

(i) 2x (3x + 2)              (ii) -1 (3x + 2)

6. Place the numbers outside both brackets together into one bracket:

(2x - 1)

7. Final answer:

6x² + x - 2 = (2x - 1) (3x + 2)