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

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


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

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

Combine like terms: n + 5n = 6n
7 + 6n = 2(2n + 1) + 3n + -2

Reorder the terms:
7 + 6n = 2(1 + 2n) + 3n + -2
7 + 6n = (1 * 2 + 2n * 2) + 3n + -2
7 + 6n = (2 + 4n) + 3n + -2

Reorder the terms:
7 + 6n = 2 + -2 + 4n + 3n

Combine like terms: 2 + -2 = 0
7 + 6n = 0 + 4n + 3n
7 + 6n = 4n + 3n

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

Solving
7 + 6n = 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.
7 + 6n + -7n = 7n + -7n

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

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7

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