2(n-5)=3n+3(2n+6)

Solution for 2(n-5)=3n+3(2n+6) equation:

2(n-5)=3n+3(2n+6)

We simplify the equation to the form, which is simple to understand 
2(n-5)=3n+3(2n+6)

Reorder the terms in parentheses
+(+2n-10)=3n+3*(2n+6)

Remove unnecessary parentheses
+2n-10=+3n+3+*(+2n+6+)

Reorder the terms in parentheses
+2n-10=3n+(+6n+18)

Remove unnecessary parentheses
+2n-10=+3n+6n+18

We move all terms containing n to the left and all other terms to the right. 
+2n-3n-6n=+18+10

We simplify left and right side of the equation. 
-7n=+28

We divide both sides of the equation by -7 to get n. 
n=-4