2[7-7(1-n)]6n=-16+3[6(n+1)-3n]

Solution for 2[7-7(1-n)]6n=-16+3[6(n+1)-3n] equation:

Simplifying
2[7 + -7(1 + -1n)] * 6n = -16 + 3[6(n + 1) + -3n]
2[7 + (1 * -7 + -1n * -7)] * 6n = -16 + 3[6(n + 1) + -3n]
2[7 + (-7 + 7n)] * 6n = -16 + 3[6(n + 1) + -3n]

Combine like terms: 7 + -7 = 0
2[0 + 7n] * 6n = -16 + 3[6(n + 1) + -3n]
2[7n] * 6n = -16 + 3[6(n + 1) + -3n]

Remove brackets around [7n]
2 * 7n * 6n = -16 + 3[6(n + 1) + -3n]

Reorder the terms for easier multiplication:
2 * 7 * 6n * n = -16 + 3[6(n + 1) + -3n]

Multiply 2 * 7
14 * 6n * n = -16 + 3[6(n + 1) + -3n]

Multiply 14 * 6
84n * n = -16 + 3[6(n + 1) + -3n]

Multiply n * n
84n2 = -16 + 3[6(n + 1) + -3n]

Reorder the terms:
84n2 = -16 + 3[6(1 + n) + -3n]
84n2 = -16 + 3[(1 * 6 + n * 6) + -3n]
84n2 = -16 + 3[(6 + 6n) + -3n]

Combine like terms: 6n + -3n = 3n
84n2 = -16 + 3[6 + 3n]
84n2 = -16 + [6 * 3 + 3n * 3]
84n2 = -16 + [18 + 9n]

Combine like terms: -16 + 18 = 2
84n2 = 2 + 9n

Solving
84n2 = 2 + 9n

Solving for variable 'n'.

Reorder the terms:
-2 + -9n + 84n2 = 2 + 9n + -2 + -9n

Reorder the terms:
-2 + -9n + 84n2 = 2 + -2 + 9n + -9n

Combine like terms: 2 + -2 = 0
-2 + -9n + 84n2 = 0 + 9n + -9n
-2 + -9n + 84n2 = 9n + -9n

Combine like terms: 9n + -9n = 0
-2 + -9n + 84n2 = 0

Begin completing the square.  Divide all terms by
84 the coefficient of the squared term: 

Divide each side by '84'.
-0.02380952381 + -0.1071428571n + n2 = 0

Move the constant term to the right:

Add '0.02380952381' to each side of the equation.
-0.02380952381 + -0.1071428571n + 0.02380952381 + n2 = 0 + 0.02380952381

Reorder the terms:
-0.02380952381 + 0.02380952381 + -0.1071428571n + n2 = 0 + 0.02380952381

Combine like terms: -0.02380952381 + 0.02380952381 = 0.00000000000
0.00000000000 + -0.1071428571n + n2 = 0 + 0.02380952381
-0.1071428571n + n2 = 0 + 0.02380952381

Combine like terms: 0 + 0.02380952381 = 0.02380952381
-0.1071428571n + n2 = 0.02380952381

The n term is -0.1071428571n.  Take half its coefficient (-0.05357142855).
Square it (0.002869897957) and add it to both sides.

Add '0.002869897957' to each side of the equation.
-0.1071428571n + 0.002869897957 + n2 = 0.02380952381 + 0.002869897957

Reorder the terms:
0.002869897957 + -0.1071428571n + n2 = 0.02380952381 + 0.002869897957

Combine like terms: 0.02380952381 + 0.002869897957 = 0.026679421767
0.002869897957 + -0.1071428571n + n2 = 0.026679421767

Factor a perfect square on the left side:
(n + -0.05357142855)(n + -0.05357142855) = 0.026679421767

Calculate the square root of the right side: 0.163338366

Break this problem into two subproblems by setting 
(n + -0.05357142855) equal to 0.163338366 and -0.163338366.

Subproblem 1
n + -0.05357142855 = 0.163338366

Simplifying
n + -0.05357142855 = 0.163338366

Reorder the terms:
-0.05357142855 + n = 0.163338366

Solving
-0.05357142855 + n = 0.163338366

Solving for variable 'n'.

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

Add '0.05357142855' to each side of the equation.
-0.05357142855 + 0.05357142855 + n = 0.163338366 + 0.05357142855

Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000
0.00000000000 + n = 0.163338366 + 0.05357142855
n = 0.163338366 + 0.05357142855

Combine like terms: 0.163338366 + 0.05357142855 = 0.21690979455
n = 0.21690979455

Simplifying
n = 0.21690979455

Subproblem 2
n + -0.05357142855 = -0.163338366

Simplifying
n + -0.05357142855 = -0.163338366

Reorder the terms:
-0.05357142855 + n = -0.163338366

Solving
-0.05357142855 + n = -0.163338366

Solving for variable 'n'.

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

Add '0.05357142855' to each side of the equation.
-0.05357142855 + 0.05357142855 + n = -0.163338366 + 0.05357142855

Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000
0.00000000000 + n = -0.163338366 + 0.05357142855
n = -0.163338366 + 0.05357142855

Combine like terms: -0.163338366 + 0.05357142855 = -0.10976693745
n = -0.10976693745

Simplifying
n = -0.10976693745

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.21690979455, -0.10976693745}