-35-8n=7(1-6n)8n

Solution for -35-8n=7(1-6n)8n equation:

Simplifying
-35 + -8n = 7(1 + -6n) * 8n

Reorder the terms for easier multiplication:
-35 + -8n = 7 * 8n(1 + -6n)

Multiply 7 * 8
-35 + -8n = 56n(1 + -6n)
-35 + -8n = (1 * 56n + -6n * 56n)
-35 + -8n = (56n + -336n2)

Solving
-35 + -8n = 56n + -336n2

Solving for variable 'n'.

Combine like terms: -8n + -56n = -64n
-35 + -64n + 336n2 = 56n + -336n2 + -56n + 336n2

Reorder the terms:
-35 + -64n + 336n2 = 56n + -56n + -336n2 + 336n2

Combine like terms: 56n + -56n = 0
-35 + -64n + 336n2 = 0 + -336n2 + 336n2
-35 + -64n + 336n2 = -336n2 + 336n2

Combine like terms: -336n2 + 336n2 = 0
-35 + -64n + 336n2 = 0

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

Divide each side by '336'.
-0.1041666667 + -0.1904761905n + n2 = 0

Move the constant term to the right:

Add '0.1041666667' to each side of the equation.
-0.1041666667 + -0.1904761905n + 0.1041666667 + n2 = 0 + 0.1041666667

Reorder the terms:
-0.1041666667 + 0.1041666667 + -0.1904761905n + n2 = 0 + 0.1041666667

Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000
0.0000000000 + -0.1904761905n + n2 = 0 + 0.1041666667
-0.1904761905n + n2 = 0 + 0.1041666667

Combine like terms: 0 + 0.1041666667 = 0.1041666667
-0.1904761905n + n2 = 0.1041666667

The n term is -0.1904761905n.  Take half its coefficient (-0.09523809525).
Square it (0.009070294787) and add it to both sides.

Add '0.009070294787' to each side of the equation.
-0.1904761905n + 0.009070294787 + n2 = 0.1041666667 + 0.009070294787

Reorder the terms:
0.009070294787 + -0.1904761905n + n2 = 0.1041666667 + 0.009070294787

Combine like terms: 0.1041666667 + 0.009070294787 = 0.113236961487
0.009070294787 + -0.1904761905n + n2 = 0.113236961487

Factor a perfect square on the left side:
(n + -0.09523809525)(n + -0.09523809525) = 0.113236961487

Calculate the square root of the right side: 0.336507001

Break this problem into two subproblems by setting 
(n + -0.09523809525) equal to 0.336507001 and -0.336507001.

Subproblem 1
n + -0.09523809525 = 0.336507001

Simplifying
n + -0.09523809525 = 0.336507001

Reorder the terms:
-0.09523809525 + n = 0.336507001

Solving
-0.09523809525 + n = 0.336507001

Solving for variable 'n'.

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

Add '0.09523809525' to each side of the equation.
-0.09523809525 + 0.09523809525 + n = 0.336507001 + 0.09523809525

Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000
0.00000000000 + n = 0.336507001 + 0.09523809525
n = 0.336507001 + 0.09523809525

Combine like terms: 0.336507001 + 0.09523809525 = 0.43174509625
n = 0.43174509625

Simplifying
n = 0.43174509625

Subproblem 2
n + -0.09523809525 = -0.336507001

Simplifying
n + -0.09523809525 = -0.336507001

Reorder the terms:
-0.09523809525 + n = -0.336507001

Solving
-0.09523809525 + n = -0.336507001

Solving for variable 'n'.

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

Add '0.09523809525' to each side of the equation.
-0.09523809525 + 0.09523809525 + n = -0.336507001 + 0.09523809525

Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000
0.00000000000 + n = -0.336507001 + 0.09523809525
n = -0.336507001 + 0.09523809525

Combine like terms: -0.336507001 + 0.09523809525 = -0.24126890575
n = -0.24126890575

Simplifying
n = -0.24126890575

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.43174509625, -0.24126890575}