Mathematica Generic and Non-Generic Solutions

2 x == 0,

it is perfectly clear that the only possible solution is x->0.

However, if you have an equation like a a x == 0.

things are not so clear,

If the a is not equal to zero, then x->0. is again the only answer.

If a is in fact equal to zero,

then any value of x is a solution, You can see this by Reduce

 

A basic difference between Reduce and Solve is that Reduce gives all the possible solutions to a set of equations, while Solve gives only the generic ones. Solutions are considered \[OpenCurlyDoubleQuote]generic\[CloseCurlyDoubleQuote] if they involve conditions only on the variables that you explicitly solve for, and not on other parameters in the equations. Reduce and Solve also differ in that Reduce always returns combinations of equations, while Solve gives results in the form of transformation rules.