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

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


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

Combine like terms: 7 + -2 = 5
2[5 + 2n] + 8n = -6 + 3[6(n + 1) + -3n]
[5 * 2 + 2n * 2] + 8n = -6 + 3[6(n + 1) + -3n]
[10 + 4n] + 8n = -6 + 3[6(n + 1) + -3n]

Combine like terms: 4n + 8n = 12n
10 + 12n = -6 + 3[6(n + 1) + -3n]

Reorder the terms:
10 + 12n = -6 + 3[6(1 + n) + -3n]
10 + 12n = -6 + 3[(1 * 6 + n * 6) + -3n]
10 + 12n = -6 + 3[(6 + 6n) + -3n]

Combine like terms: 6n + -3n = 3n
10 + 12n = -6 + 3[6 + 3n]
10 + 12n = -6 + [6 * 3 + 3n * 3]
10 + 12n = -6 + [18 + 9n]

Combine like terms: -6 + 18 = 12
10 + 12n = 12 + 9n

Solving
10 + 12n = 12 + 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.
10 + 12n + -9n = 12 + 9n + -9n

Combine like terms: 12n + -9n = 3n
10 + 3n = 12 + 9n + -9n

Combine like terms: 9n + -9n = 0
10 + 3n = 12 + 0
10 + 3n = 12

Add '-10' to each side of the equation.
10 + -10 + 3n = 12 + -10

Combine like terms: 10 + -10 = 0
0 + 3n = 12 + -10
3n = 12 + -10

Combine like terms: 12 + -10 = 2
3n = 2

Divide each side by '3'.
n = 0.6666666667

Simplifying
n = 0.6666666667

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