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

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


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

Reorder the terms:
2(1 + 2n) + n = 5n + 7 + 3n + -2
(1 * 2 + 2n * 2) + n = 5n + 7 + 3n + -2
(2 + 4n) + n = 5n + 7 + 3n + -2

Combine like terms: 4n + n = 5n
2 + 5n = 5n + 7 + 3n + -2

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

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

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

Solving
2 + 5n = 5 + 8n

Solving for variable 'n'.

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

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

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

Combine like terms: 8n + -8n = 0
2 + -3n = 5 + 0
2 + -3n = 5

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

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

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

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

Simplifying
n = -1

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