Solve 3x^2 + 6x + 3 = 0

Since there is a common factor of 3 on the the left hand side of the equation, you can take that out as a factor:
3(x^2 + 2x +1) = 0
Then you you can divide both sides by 3:
x^2 + 2x + 1 = 0
Now you need to find two number that add to make 2 and multiply to make 1: (x + ?)(x + ?) = 0 - these two numbers are 1 and 1 so, (x+1)(x+1) = 0
To multiply a two number and get a 0, at least one number must be 0:
(x+1) = 0 or (x+1) = 0
Moving 1 to the other side you are left with x = -1
Now to check:
(-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0
Your answer is therefore true!