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I am not entirely sure what situation you are talking about. If there is no "x" in an equation, there is no point in finding it.
On the other hand, if "x" disappears when solving an equation, that's usually an indication that the equation is always true, or always false, independently of the value of "x". Example:
x = x + 1
Subtracting "x" from both sides, you get:
0 = 1
Since this is false, the equation is false (for ANY value of "x"). As another example:
3x = 3x
Subtracing 3x on each side, you get:
0 = 0
Since this is true, and "x" doesn't appear in it, the original equation is ALWAYS true, i.e., no matter what value "x" has.
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