3(n+2)+3(n-2)+1=13

Solution for 3(n+2)+3(n-2)+1=13 equation:

Simplifying
3(n + 2) + 3(n + -2) + 1 = 13

Reorder the terms:
3(2 + n) + 3(n + -2) + 1 = 13
(2 * 3 + n * 3) + 3(n + -2) + 1 = 13
(6 + 3n) + 3(n + -2) + 1 = 13

Reorder the terms:
6 + 3n + 3(-2 + n) + 1 = 13
6 + 3n + (-2 * 3 + n * 3) + 1 = 13
6 + 3n + (-6 + 3n) + 1 = 13

Reorder the terms:
6 + -6 + 1 + 3n + 3n = 13

Combine like terms: 6 + -6 = 0
0 + 1 + 3n + 3n = 13
1 + 3n + 3n = 13

Combine like terms: 3n + 3n = 6n
1 + 6n = 13

Solving
1 + 6n = 13

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 6n = 13 + -1

Combine like terms: 1 + -1 = 0
0 + 6n = 13 + -1
6n = 13 + -1

Combine like terms: 13 + -1 = 12
6n = 12

Divide each side by '6'.
n = 2

Simplifying
n = 2