find the values of x when 3x^2 - 6x - 9

First we will need to factorise the equation.

Start with the 3x^2 term and notice 3 is prime so must have 3x and x terms.

(3x - 9) (x + 1) or  (3x + 3) (x - 3)

Setting the brackets to 0 gives us 3x - 9 = 0 and x + 1 = 0   or  3x + 3 = 0 and x - 3 = 0

meaning  x = 3 and x = -1