Don't understand algebraic equation

Hi Linnea, I'm Josh.

Let's pick up from here: -6 = 2x-6
We're trying to get the variable x on one side and the numbers on the other, right? So to get rid of the -6 that's on the right-hand side, we can add a +6. But we have to add a +6 to the left-hand side, also, to maintain equality:

-6 = 2x-6
-6 +6 = 2x-6+6 (add a 6 to each side)

It just so happens in this equation that adding a +6 to each side makes the left hand side 0, also, but it didn't have to be that way. So now from where we left off, combining:
-6+6 = 2x-6+6
0 = 2x

We can switch the sides of an equality any time, so from
0 = 2x we can also say
2x = 0

And from there, we divide both sides by 2. On the left that leaves us with x (2x/2) and on the right, we still have 0, because 0 divided by 2 is still 0:

So, x = 0.

Let me know if this wasn't clear enough, I'll be happy to try something else or try to find a video to direct you to.