What Is The Short Cut For 19-(2x+3)=2(x+3)+x?

There is no such short cut for these problems but they become very easy if you proceed systematically. Remember the rule of BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction)?
So, first open all the brackets in any equation:

Your question:
19 - (2x+3) = 2(x + 3) + x

Solution:
Brackets first:
19 - 2x - 3 = 2x + 6 + x

Now, it is very simple, just take the x values on one side and the others on the other side:

2x + 2x + x = 19 - 3 - 6
5x = 10
x = 10/2
x = 5

Your answer is x=5.