Einstein's 1916/1962 derivation (Appendix A of Relativity:  The Special and
General Theory) of the BEER (Basic Equations of Einstein's Relativity)
starts with x=-ct and x=ct (as well as another such pair of contradictory
simultaneous equations: x'=-ct' and x'=ct').

If you understand simultaneous equations you understand that the usual point
is to see if there is a common solution or maybe a set of common solutions.

The pair,  x=ct and x=-ct, given that c is know to be a positive number,
immediately tell us that x must be zero, and x'=-ct' and x'=ct' prove that
x' must be zero.  Similarly for t and t', which must both be zero for x and
x' to be zero.

Obviously, any conclusion, derivation, based on these equation pairs must be
valid, if valid at all, for x=0 and x'=0.

That is so obvious I never bothered giving obvious examples, but obvious or
not Relativity-cult cretins lambasted me, declaring there was no problem
with the use of such equation pairs.

[...]

 See also

https://home.deds.nl/~dvdm/dirk/Physics/Fumbles/Crimes.html

http://groups-beta.google.com/group/sci.physics/msg/5d6c47f606f4dd30