2(n+1)=3(5n+4)+7n

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Solution for 2(n+1)=3(5n+4)+7n equation: 


Simplifying
2(n + 1) = 3(5n + 4) + 7n

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

Reorder the terms:
2 + 2n = 3(4 + 5n) + 7n
2 + 2n = (4 * 3 + 5n * 3) + 7n
2 + 2n = (12 + 15n) + 7n

Combine like terms: 15n + 7n = 22n
2 + 2n = 12 + 22n

Solving
2 + 2n = 12 + 22n

Solving for variable 'n'.

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

Add '-22n' to each side of the equation.
2 + 2n + -22n = 12 + 22n + -22n

Combine like terms: 2n + -22n = -20n
2 + -20n = 12 + 22n + -22n

Combine like terms: 22n + -22n = 0
2 + -20n = 12 + 0
2 + -20n = 12

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

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

Combine like terms: 12 + -2 = 10
-20n = 10

Divide each side by '-20'.
n = -0.5

Simplifying
n = -0.5

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