I have already looked for many answers but none of them appears to satisfy my question.
I can imagine why everything divided by 0 makes no sense and has no solution.
x divided by 0 means that you divide by nothing and therefore do not divide anything, so there is no answer available as you do not do anything. In other words, you are still left with your x / 0 waiting, stuck in time for infinity.
Now I want to understand why x times 0 is possible and equals 0.
I mean 1 times x = x (How many times do I add x? once, therefore x); 2 * x (How many times do I add x? Twice. therefore x + x). Now what about 0 * x? How many times? Not any time at all. Shouldn't this also be regarded as an impossible operation? You still don't do anything and are stuck in time for infinity, so why do we have an answer here? Please don't say "because this is how it is defined". I don't like that type of answers.
If the answer is "how many times? 0 times, therefore 0, then this can also be applied to division and then say how many apples to you give John? none, so 0. However, it is impossible to divide by 0.