(2n+1)+(2n+3)+(2n+5)=57

Solution for (2n+1)+(2n+3)+(2n+5)=57 equation:

Simplifying
(2n + 1) + (2n + 3) + (2n + 5) = 57

Reorder the terms:
(1 + 2n) + (2n + 3) + (2n + 5) = 57

Remove parenthesis around (1 + 2n)
1 + 2n + (2n + 3) + (2n + 5) = 57

Reorder the terms:
1 + 2n + (3 + 2n) + (2n + 5) = 57

Remove parenthesis around (3 + 2n)
1 + 2n + 3 + 2n + (2n + 5) = 57

Reorder the terms:
1 + 2n + 3 + 2n + (5 + 2n) = 57

Remove parenthesis around (5 + 2n)
1 + 2n + 3 + 2n + 5 + 2n = 57

Reorder the terms:
1 + 3 + 5 + 2n + 2n + 2n = 57

Combine like terms: 1 + 3 = 4
4 + 5 + 2n + 2n + 2n = 57

Combine like terms: 4 + 5 = 9
9 + 2n + 2n + 2n = 57

Combine like terms: 2n + 2n = 4n
9 + 4n + 2n = 57

Combine like terms: 4n + 2n = 6n
9 + 6n = 57

Solving
9 + 6n = 57

Solving for variable 'n'.

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

Add '-9' to each side of the equation.
9 + -9 + 6n = 57 + -9

Combine like terms: 9 + -9 = 0
0 + 6n = 57 + -9
6n = 57 + -9

Combine like terms: 57 + -9 = 48
6n = 48

Divide each side by '6'.
n = 8

Simplifying
n = 8