How does factorials work in algebraic equations?

Question

I was reading a text book and found these two lines and I have no clue how did step1 become step2. Please help me with this. Thanks

Step 1:

$$ \frac {5!}{(4-r)!} = \frac {6*5!}{(5-r+1)(5-r)(5-r-1)!} $$

Step 2: $$ (6-r)(5-r)=6 $$

Text book: (NCERT 11th Chapter 7, Example 13)

Answer 1

First things first: Simplify.

If we simplify the first step, we have $$\frac{5!}{(4-r)!}=\frac{6 \times 5!}{(6-r)(5-r)(4-r)!}$$

Now multiply each side by $\frac{(6-r)(5-4)(4-r)!}{5!}$.

Thus we have $$\frac {5!}{(4-r)!} = \frac {6*5!}{(5-r+1)(5-r)(5-r-1)!} \Leftrightarrow (6-r)(5-r)=6$$