Answer:
x = 3, x = 1
Explanation:
Okay, let's set the equation = 0:
3x^2 -12x + 9 = 0
Then, we factorise. To do this, we have to find 2 numbers which have a product of 9 and add up to -12. There are a few ways to do this, but a simple try and error is the easier when using numbers which don't have many factors. So here we know that to get a product of 9, there are only 2 options: 9*1 and 3*3. Now we have to figure out which of these add up to -12. But to do this, we have to take into account the 3, from the x^2 coefficient. This allows to know that the numbers will be 9*1. Then we just need to change the signs to make it work. This would give: -9*-1 (with 3*-1).
The fully factorised equation would be (3x-9)(x-1). Following this, you can always expand it quickly, to check that it really works correctly.
Now let's solve. (3x-9)(x-1) = 0
We say that when two numbers multiplied by each other equal to zero, one of them has to be zero. So if (3x - 9) was equal to 0:
3x - 9 = 0
3x = 9
x = 9/3
x = 3/1
x = 3
Now for the other:
x - 1 = 0
x = 1