3n-2+5n+7=2(2n+1)+n

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Solution for 3n-2+5n+7=2(2n+1)+n equation:


Simplifying
3n + -2 + 5n + 7 = 2(2n + 1) + n

Reorder the terms:
-2 + 7 + 3n + 5n = 2(2n + 1) + n

Combine like terms: -2 + 7 = 5
5 + 3n + 5n = 2(2n + 1) + n

Combine like terms: 3n + 5n = 8n
5 + 8n = 2(2n + 1) + n

Reorder the terms:
5 + 8n = 2(1 + 2n) + n
5 + 8n = (1 * 2 + 2n * 2) + n
5 + 8n = (2 + 4n) + n

Combine like terms: 4n + n = 5n
5 + 8n = 2 + 5n

Solving
5 + 8n = 2 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
5 + 8n + -5n = 2 + 5n + -5n

Combine like terms: 8n + -5n = 3n
5 + 3n = 2 + 5n + -5n

Combine like terms: 5n + -5n = 0
5 + 3n = 2 + 0
5 + 3n = 2

Add '-5' to each side of the equation.
5 + -5 + 3n = 2 + -5

Combine like terms: 5 + -5 = 0
0 + 3n = 2 + -5
3n = 2 + -5

Combine like terms: 2 + -5 = -3
3n = -3

Divide each side by '3'.
n = -1

Simplifying
n = -1

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