The solution is supposed to tell you what "x" is and you can't very well do that if you subtract it from both sides so you must leave it in the original form. Then what is "x"? Just like what is x♠2 = √-1 You can't find "x" so this whole equation is defining a new number system , exactly the way imaginary numbers were defined. 3-4(2-3X) = 2(6x+2) x is a number, It is the number in the equation. You can't write this equation as "x= a number" but you can leave it in its original form. Here is also an equation in which the rules of algebra fail. You can't always subract the 12x from both sides, I think this is the addition property of equality. so If i do an experiment and try different values of "x" I would probably get a fuzzy answer. If I put a very large number as "x" the answer approaches equality so X is probably infinite. But I don't believe infinity exists because of quantum uncertainties. Points or zero and infinity do not exist in the real world so how can mathematicians use concepts that are physically impossible. So if you try any number , not infinity in the equation then you get two different values for "x" . The equation needs two different values for the same variable. Just like quantum mechanics where a particle can be in two different places at the same time.