6x-(x-3)=3(2x-4)-(x+1)

Solution for 6x-(x-3)=3(2x-4)-(x+1) equation:

6x-(x-3)=3 (2x-4)-(x+1)

We simplify the equation to the form, which is simple to understand 
6x-(x-3)=3(2x-4)-(x+1)

Remove unnecessary parentheses
6x-1x+3=3*(2x-4)-(x+1)

Reorder the terms in parentheses
6x-1x+3=+(+6x-12)-(x+1)

Remove unnecessary parentheses
+6x-1x+3=+6x-12-(+x+1+)

Remove unnecessary parentheses
6x-1x+3=+6x-12-1x-1

We move all terms containing x to the left and all other terms to the right. 
+6x-1x-6x+1x=-12-1-3

We simplify left and right side of the equation. 
0x=-16

0=-16

The left and right sides are not equal, therefore there is no solution. This equation is invalid.