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HELP! Factor completely. 3x^2 + 12x + 9

Mathematics
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So for example 3w^2 + 12w + 9 = 3(w^2 + 4w +3) = 3(w^2 + w + 3w + 3) <- how did they get this part?
Looks like they just separated 4w into w + 3w ?

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Other answers:

But if you are asking why they chose to do it that way, it is because this particular arrangement allows you to factor w^2 + w + 3w + w into w(w + 1) + 3(w + 1) = (w + 1)(w + 3). Alternatively you could have looked at w^2 + 4w + 3 and ask what two numbers multiply to 3 and add to 4? 1 and 3 Thus w^2 + 4w + 3 = (w + 1)(w + 3)
Ohhh... Thank you so much!
I meant to say: w^2 + w + 3w + "3" into w(w + 1) + 3(w + 1)
I will correct that to avoid ambiguity
Er..cannot edit posts here ;( nvm.

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