Where lies the flaw in the logic?

A Proof That 2 = 0:

1. X = 2 let x=2
2. X*X = 2X multiply by x on both sides
3. X*X - 4 = 2X - 4 subtract 4 from both sides
4. (X+2)(X-2) = 2(X-2) factorise
5. X+2 = 2 divide by (x-2) on both sides
6. X = 0 subtract 2 from both sides


Therefore x=2 and x=0 at the same time! Where lies the flaw in the logic?

The problem is with the fourth step.

(X+2)(X-2) = 2(X-2)
because values of x-2 is zero. you can't facotrise zero in an equation

Even though, 4 * 0 = 2 *0 =0 it does not meen that 4=2