2[7-3(1-n)]+6n=8+3[6(n+1)-3n]

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Solution for 2[7-3(1-n)]+6n=8+3[6(n+1)-3n] equation:


Simplifying
2[7 + -3(1 + -1n)] + 6n = 8 + 3[6(n + 1) + -3n]
2[7 + (1 * -3 + -1n * -3)] + 6n = 8 + 3[6(n + 1) + -3n]
2[7 + (-3 + 3n)] + 6n = 8 + 3[6(n + 1) + -3n]

Combine like terms: 7 + -3 = 4
2[4 + 3n] + 6n = 8 + 3[6(n + 1) + -3n]
[4 * 2 + 3n * 2] + 6n = 8 + 3[6(n + 1) + -3n]
[8 + 6n] + 6n = 8 + 3[6(n + 1) + -3n]

Combine like terms: 6n + 6n = 12n
8 + 12n = 8 + 3[6(n + 1) + -3n]

Reorder the terms:
8 + 12n = 8 + 3[6(1 + n) + -3n]
8 + 12n = 8 + 3[(1 * 6 + n * 6) + -3n]
8 + 12n = 8 + 3[(6 + 6n) + -3n]

Combine like terms: 6n + -3n = 3n
8 + 12n = 8 + 3[6 + 3n]
8 + 12n = 8 + [6 * 3 + 3n * 3]
8 + 12n = 8 + [18 + 9n]

Combine like terms: 8 + 18 = 26
8 + 12n = 26 + 9n

Solving
8 + 12n = 26 + 9n

Solving for variable 'n'.

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

Add '-9n' to each side of the equation.
8 + 12n + -9n = 26 + 9n + -9n

Combine like terms: 12n + -9n = 3n
8 + 3n = 26 + 9n + -9n

Combine like terms: 9n + -9n = 0
8 + 3n = 26 + 0
8 + 3n = 26

Add '-8' to each side of the equation.
8 + -8 + 3n = 26 + -8

Combine like terms: 8 + -8 = 0
0 + 3n = 26 + -8
3n = 26 + -8

Combine like terms: 26 + -8 = 18
3n = 18

Divide each side by '3'.
n = 6

Simplifying
n = 6

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