-3(6n+1)-2(7n-2)3(1n+5)=5(2n-1)

Solution for -3(6n+1)-2(7n-2)3(1n+5)=5(2n-1) equation:

Simplifying
-3(6n + 1) + -2(7n + -2) * 3(1n + 5) = 5(2n + -1)

Reorder the terms:
-3(1 + 6n) + -2(7n + -2) * 3(1n + 5) = 5(2n + -1)
(1 * -3 + 6n * -3) + -2(7n + -2) * 3(1n + 5) = 5(2n + -1)
(-3 + -18n) + -2(7n + -2) * 3(1n + 5) = 5(2n + -1)

Reorder the terms:
-3 + -18n + -2(-2 + 7n) * 3(1n + 5) = 5(2n + -1)

Reorder the terms:
-3 + -18n + -2(-2 + 7n) * 3(5 + 1n) = 5(2n + -1)

Reorder the terms for easier multiplication:
-3 + -18n + -2 * 3(-2 + 7n)(5 + 1n) = 5(2n + -1)

Multiply -2 * 3
-3 + -18n + -6(-2 + 7n)(5 + 1n) = 5(2n + -1)

Multiply (-2 + 7n) * (5 + 1n)
-3 + -18n + -6(-2(5 + 1n) + 7n * (5 + 1n)) = 5(2n + -1)
-3 + -18n + -6((5 * -2 + 1n * -2) + 7n * (5 + 1n)) = 5(2n + -1)
-3 + -18n + -6((-10 + -2n) + 7n * (5 + 1n)) = 5(2n + -1)
-3 + -18n + -6(-10 + -2n + (5 * 7n + 1n * 7n)) = 5(2n + -1)
-3 + -18n + -6(-10 + -2n + (35n + 7n2)) = 5(2n + -1)

Combine like terms: -2n + 35n = 33n
-3 + -18n + -6(-10 + 33n + 7n2) = 5(2n + -1)
-3 + -18n + (-10 * -6 + 33n * -6 + 7n2 * -6) = 5(2n + -1)
-3 + -18n + (60 + -198n + -42n2) = 5(2n + -1)

Reorder the terms:
-3 + 60 + -18n + -198n + -42n2 = 5(2n + -1)

Combine like terms: -3 + 60 = 57
57 + -18n + -198n + -42n2 = 5(2n + -1)

Combine like terms: -18n + -198n = -216n
57 + -216n + -42n2 = 5(2n + -1)

Reorder the terms:
57 + -216n + -42n2 = 5(-1 + 2n)
57 + -216n + -42n2 = (-1 * 5 + 2n * 5)
57 + -216n + -42n2 = (-5 + 10n)

Solving
57 + -216n + -42n2 = -5 + 10n

Solving for variable 'n'.

Reorder the terms:
57 + 5 + -216n + -10n + -42n2 = -5 + 10n + 5 + -10n

Combine like terms: 57 + 5 = 62
62 + -216n + -10n + -42n2 = -5 + 10n + 5 + -10n

Combine like terms: -216n + -10n = -226n
62 + -226n + -42n2 = -5 + 10n + 5 + -10n

Reorder the terms:
62 + -226n + -42n2 = -5 + 5 + 10n + -10n

Combine like terms: -5 + 5 = 0
62 + -226n + -42n2 = 0 + 10n + -10n
62 + -226n + -42n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
62 + -226n + -42n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + -113n + -21n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(31 + -113n + -21n2)' equal to zero and attempt to solve:

Simplifying
31 + -113n + -21n2 = 0

Solving
31 + -113n + -21n2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-1.476190476 + 5.380952381n + n2 = 0

Move the constant term to the right:

Add '1.476190476' to each side of the equation.
-1.476190476 + 5.380952381n + 1.476190476 + n2 = 0 + 1.476190476

Reorder the terms:
-1.476190476 + 1.476190476 + 5.380952381n + n2 = 0 + 1.476190476

Combine like terms: -1.476190476 + 1.476190476 = 0.000000000
0.000000000 + 5.380952381n + n2 = 0 + 1.476190476
5.380952381n + n2 = 0 + 1.476190476

Combine like terms: 0 + 1.476190476 = 1.476190476
5.380952381n + n2 = 1.476190476

The n term is 5.380952381n.  Take half its coefficient (2.690476191).
Square it (7.238662134) and add it to both sides.

Add '7.238662134' to each side of the equation.
5.380952381n + 7.238662134 + n2 = 1.476190476 + 7.238662134

Reorder the terms:
7.238662134 + 5.380952381n + n2 = 1.476190476 + 7.238662134

Combine like terms: 1.476190476 + 7.238662134 = 8.71485261
7.238662134 + 5.380952381n + n2 = 8.71485261

Factor a perfect square on the left side:
(n + 2.690476191)(n + 2.690476191) = 8.71485261

Calculate the square root of the right side: 2.95209292

Break this problem into two subproblems by setting 
(n + 2.690476191) equal to 2.95209292 and -2.95209292.

Subproblem 1
n + 2.690476191 = 2.95209292

Simplifying
n + 2.690476191 = 2.95209292

Reorder the terms:
2.690476191 + n = 2.95209292

Solving
2.690476191 + n = 2.95209292

Solving for variable 'n'.

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

Add '-2.690476191' to each side of the equation.
2.690476191 + -2.690476191 + n = 2.95209292 + -2.690476191

Combine like terms: 2.690476191 + -2.690476191 = 0.000000000
0.000000000 + n = 2.95209292 + -2.690476191
n = 2.95209292 + -2.690476191

Combine like terms: 2.95209292 + -2.690476191 = 0.261616729
n = 0.261616729

Simplifying
n = 0.261616729

Subproblem 2
n + 2.690476191 = -2.95209292

Simplifying
n + 2.690476191 = -2.95209292

Reorder the terms:
2.690476191 + n = -2.95209292

Solving
2.690476191 + n = -2.95209292

Solving for variable 'n'.

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

Add '-2.690476191' to each side of the equation.
2.690476191 + -2.690476191 + n = -2.95209292 + -2.690476191

Combine like terms: 2.690476191 + -2.690476191 = 0.000000000
0.000000000 + n = -2.95209292 + -2.690476191
n = -2.95209292 + -2.690476191

Combine like terms: -2.95209292 + -2.690476191 = -5.642569111
n = -5.642569111

Simplifying
n = -5.642569111

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.261616729, -5.642569111}
Solution
n = {0.261616729, -5.642569111}