What's wrong with this "proof?"

Does there exist $x$ such that $x^2-5x+6=0$?

Solution: $x^2-5x+6=0 \ (x-2)(x-3)=0 \ x=2~\text{ or }~3~~~\blacksquare$

Question

What's wrong with this "proof?"

Does there exist $x$ such that $x^2-5x+6=0$?

Solution: $x^2-5x+6=0 \ (x-2)(x-3)=0 \ x=2~\text{  or  }~3~~~\blacksquare$

geerky42 · Answer

If I heard correctly, it's because I assumed there is value at beginning, hence assumed hypothesis is true. but I don't understand the problem with it...?

geerky42 · Answer

Does anyone have idea?

acxbox22 · Answer

it looks alright to me

geerky42 · Answer

Well, it is acceptable to normal person, but this proof is not exactly appropriate in "mathematical proof" world.

I just don't really understand why...

geerky42 · Answer

@satellite73 @abb0t @Hero 
Have any idea?