n+(n+4)+(n+8)=[3(n+8)-(n+4)]-n

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Solution for n+(n+4)+(n+8)=[3(n+8)-(n+4)]-n equation: 


Simplifying
n + (n + 4) + (n + 8) = [3(n + 8) + -1(n + 4)] + -1n

Reorder the terms:
n + (4 + n) + (n + 8) = [3(n + 8) + -1(n + 4)] + -1n

Remove parenthesis around (4 + n)
n + 4 + n + (n + 8) = [3(n + 8) + -1(n + 4)] + -1n

Reorder the terms:
n + 4 + n + (8 + n) = [3(n + 8) + -1(n + 4)] + -1n

Remove parenthesis around (8 + n)
n + 4 + n + 8 + n = [3(n + 8) + -1(n + 4)] + -1n

Reorder the terms:
4 + 8 + n + n + n = [3(n + 8) + -1(n + 4)] + -1n

Combine like terms: 4 + 8 = 12
12 + n + n + n = [3(n + 8) + -1(n + 4)] + -1n

Combine like terms: n + n = 2n
12 + 2n + n = [3(n + 8) + -1(n + 4)] + -1n

Combine like terms: 2n + n = 3n
12 + 3n = [3(n + 8) + -1(n + 4)] + -1n

Reorder the terms:
12 + 3n = [3(8 + n) + -1(n + 4)] + -1n
12 + 3n = [(8 * 3 + n * 3) + -1(n + 4)] + -1n
12 + 3n = [(24 + 3n) + -1(n + 4)] + -1n

Reorder the terms:
12 + 3n = [24 + 3n + -1(4 + n)] + -1n
12 + 3n = [24 + 3n + (4 * -1 + n * -1)] + -1n
12 + 3n = [24 + 3n + (-4 + -1n)] + -1n

Reorder the terms:
12 + 3n = [24 + -4 + 3n + -1n] + -1n

Combine like terms: 24 + -4 = 20
12 + 3n = [20 + 3n + -1n] + -1n

Combine like terms: 3n + -1n = 2n
12 + 3n = [20 + 2n] + -1n

Remove brackets around [20 + 2n]
12 + 3n = 20 + 2n + -1n

Combine like terms: 2n + -1n = 1n
12 + 3n = 20 + 1n

Solving
12 + 3n = 20 + 1n

Solving for variable 'n'.

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

Add '-1n' to each side of the equation.
12 + 3n + -1n = 20 + 1n + -1n

Combine like terms: 3n + -1n = 2n
12 + 2n = 20 + 1n + -1n

Combine like terms: 1n + -1n = 0
12 + 2n = 20 + 0
12 + 2n = 20

Add '-12' to each side of the equation.
12 + -12 + 2n = 20 + -12

Combine like terms: 12 + -12 = 0
0 + 2n = 20 + -12
2n = 20 + -12

Combine like terms: 20 + -12 = 8
2n = 8

Divide each side by '2'.
n = 4

Simplifying
n = 4

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