Why can’t we divide by x on both sides and eliminate the 1 x? That would give us 2 solutions right?
You can as long as you verify whether x = 0 is a solution afterwards.
For example, consider a similar problem like x(x - 4) = 0. You cannot divide both sides by x if x was 0. So, in order to divide both sides by x (safely), you would assume that x is anything but 0.
Finally, you must check if 0 is a solution by plugging it back into the original equation, because your entire algebraic solution hinged on the assumption that x \neq 0.
Oh yeah that makes sense, 0/0 doesn’t work. Thanks!