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

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

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

Combine like terms: 5n + n = 6n
6n = 3n + 2 + 2(2n + 1)

Reorder the terms:
6n = 3n + 2 + 2(1 + 2n)
6n = 3n + 2 + (1 * 2 + 2n * 2)
6n = 3n + 2 + (2 + 4n)

Reorder the terms:
6n = 2 + 2 + 3n + 4n

Combine like terms: 2 + 2 = 4
6n = 4 + 3n + 4n

Combine like terms: 3n + 4n = 7n
6n = 4 + 7n

Solving
6n = 4 + 7n

Solving for variable 'n'.

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

Add '-7n' to each side of the equation.
6n + -7n = 4 + 7n + -7n

Combine like terms: 6n + -7n = -1n
-1n = 4 + 7n + -7n

Combine like terms: 7n + -7n = 0
-1n = 4 + 0
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4