4(2n+1)+n=3(n+2)

Solution for 4(2n+1)+n=3(n+2) equation:

Simplifying
4(2n + 1) + n = 3(n + 2)

Reorder the terms:
4(1 + 2n) + n = 3(n + 2)
(1 * 4 + 2n * 4) + n = 3(n + 2)
(4 + 8n) + n = 3(n + 2)

Combine like terms: 8n + n = 9n
4 + 9n = 3(n + 2)

Reorder the terms:
4 + 9n = 3(2 + n)
4 + 9n = (2 * 3 + n * 3)
4 + 9n = (6 + 3n)

Solving
4 + 9n = 6 + 3n

Solving for variable 'n'.

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

Add '-3n' to each side of the equation.
4 + 9n + -3n = 6 + 3n + -3n

Combine like terms: 9n + -3n = 6n
4 + 6n = 6 + 3n + -3n

Combine like terms: 3n + -3n = 0
4 + 6n = 6 + 0
4 + 6n = 6

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

Combine like terms: 4 + -4 = 0
0 + 6n = 6 + -4
6n = 6 + -4

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

Divide each side by '6'.
n = 0.3333333333

Simplifying
n = 0.3333333333