Seeking help on probability practice question

Hey everyone, looking for pointers on the following question (see snip).

The explanation states that we set the multiplied probabilities equal to the given answer (5/14) and then solve for n. However, I’m confused why in the highlighted step “5/14” becomes “1/14.” Could any kind souls explain? Thanks in advance.

Divide by 5 on the LHS and RHS.

Thank you - could you extrapolate on why we divide by 5 here, and why this is applied to the numerator but not the denominator of the LHS and RHS of the equation?

The point is that this is actually optional. Notice that we have

\frac{20}{(n + 5)(n + 4)} = \frac{5}{14}

What we are doing is

\frac{1}{5} \times \frac{20}{(n + 5)(n + 4)} = \frac{1}{5} \times \frac{5}{14}

Do you now see how we get the result?