Proof by Induction solution not understood Here is a question and solution but I don't understand what's happening after $m = m+1$.

(source: gyazo.com)
How does $(3(m+1))!$ equal $(3m)!(3m+1)(3m+2)(3m+3)$? Should it not be $(3m+3)!$?
Same thing with the other side of the equation.
I also don't understand the equation after the "Also".

$$(3(m+1))!=(3m+3)!=1\cdot2\cdot\ldots\cdot(3m)\cdot(3m+1)\cdot(3m+2)\cdot(3m+3)=$$
$$=(3m)!(3m+1)(3m+2)(3m+3)$$
And a similar thing on the other side.
