Math question: why do they do this step in transforming a formula? (in calculating absolute zero)

from this video (at timestamp 7:36): https://youtu.be/wR2tOLShFmY?si=PRfQue1CqV5AG8fE&t=456 about calculating the value of absolute zero by measuring the volume of a gas at 2 different temperatures.
We’re coming up with a single formula that takes in the temperatures and volumes at the two different points (T1/T2 and V1/V2, respectively)

Our base formula is
V/a = x+T (I’ll explain a at the end, it’s a constant that is the same at both measurements)
Then, for our specific measurements, the formulas are:
V1/a=X+T1
V2/a=x+T2

Then, we multiply both sides of the second formula by (V1/V2). Why? What is the principle or logic for picking that operator? Sure, it’s a valid operation (generally you can do whatever you want to an equation as long as you do it to both sides), I just don’t get the logical leap there.

trivia:‘a’ in this formula represents the ‘nR/P’ portion of the ideal gas law.

To turn the left side into V1/a, matching the left side of the first equation. You then get two expressions that are both equal to V1/a, so you can set them equal to each other (or equivalently, set their difference equal to 0, which is how the video does it).

Multiplying by V1/V2 is equivalent to dividing by V2 and multiplying by V1.

ah-HA!! Yes!! Now it makes sense.

Thank you very much.