Don't forget the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
In the case of
(4+2(-5)+3(2+(-3))+2)6+(-2),
which should be written as 6[4+2(-5)+3(2+[-3])+2]+(-2),
First:
6[4+2(-5)+3(2+[-3])+2]+(-2) --> The bolded terms can become 2-3, which is -1. You are doing the parentheses first, and that is the smallest parentheses term you can simplify.
Now you have 6[4+2(-5)+3(-1)+2]+(-2).
Continue inside the parentheses, but now with multiplication (in this case you're doing the order of operations within the order of operations!):
6[4+2(-5)+3(-1)+2]+(-2) --> The bolded areas are 2 x -5, which becomes -10; and 3 x -1, which becomes -3.
You now have: 6[4+(-10)+(-3)+2]+(-2)
You should never have something plus a negative, because that can simplify to minus a positive.
You now have: 6[4-10-3+2]-2
Simply complete the addition or subtraction within the parentheses in the order it is shown from left to right:
6[-6-3+2]-2
6[-9+2]-2
6[-7]-2
Now, multiplication comes before subtraction in the order of operations. So, multiply 6 x -7:
-42-2
Simply subtract:
-44
And there you have your final answer!
