2(9n-1)7(n+6)=-60

Solution for 2(9n-1)7(n+6)=-60 equation:

Simplifying
2(9n + -1) * 7(n + 6) = -60

Reorder the terms:
2(-1 + 9n) * 7(n + 6) = -60

Reorder the terms:
2(-1 + 9n) * 7(6 + n) = -60

Reorder the terms for easier multiplication:
2 * 7(-1 + 9n)(6 + n) = -60

Multiply 2 * 7
14(-1 + 9n)(6 + n) = -60

Multiply (-1 + 9n) * (6 + n)
14(-1(6 + n) + 9n * (6 + n)) = -60
14((6 * -1 + n * -1) + 9n * (6 + n)) = -60
14((-6 + -1n) + 9n * (6 + n)) = -60
14(-6 + -1n + (6 * 9n + n * 9n)) = -60
14(-6 + -1n + (54n + 9n2)) = -60

Combine like terms: -1n + 54n = 53n
14(-6 + 53n + 9n2) = -60
(-6 * 14 + 53n * 14 + 9n2 * 14) = -60
(-84 + 742n + 126n2) = -60

Solving
-84 + 742n + 126n2 = -60

Solving for variable 'n'.

Reorder the terms:
-84 + 60 + 742n + 126n2 = -60 + 60

Combine like terms: -84 + 60 = -24
-24 + 742n + 126n2 = -60 + 60

Combine like terms: -60 + 60 = 0
-24 + 742n + 126n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 371n + 63n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + 371n + 63n2)' equal to zero and attempt to solve:

Simplifying
-12 + 371n + 63n2 = 0

Solving
-12 + 371n + 63n2 = 0

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

Divide each side by '63'.
-0.1904761905 + 5.888888889n + n2 = 0

Move the constant term to the right:

Add '0.1904761905' to each side of the equation.
-0.1904761905 + 5.888888889n + 0.1904761905 + n2 = 0 + 0.1904761905

Reorder the terms:
-0.1904761905 + 0.1904761905 + 5.888888889n + n2 = 0 + 0.1904761905

Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000
0.0000000000 + 5.888888889n + n2 = 0 + 0.1904761905
5.888888889n + n2 = 0 + 0.1904761905

Combine like terms: 0 + 0.1904761905 = 0.1904761905
5.888888889n + n2 = 0.1904761905

The n term is 5.888888889n.  Take half its coefficient (2.944444445).
Square it (8.669753090) and add it to both sides.

Add '8.669753090' to each side of the equation.
5.888888889n + 8.669753090 + n2 = 0.1904761905 + 8.669753090

Reorder the terms:
8.669753090 + 5.888888889n + n2 = 0.1904761905 + 8.669753090

Combine like terms: 0.1904761905 + 8.669753090 = 8.8602292805
8.669753090 + 5.888888889n + n2 = 8.8602292805

Factor a perfect square on the left side:
(n + 2.944444445)(n + 2.944444445) = 8.8602292805

Calculate the square root of the right side: 2.976613727

Break this problem into two subproblems by setting 
(n + 2.944444445) equal to 2.976613727 and -2.976613727.

Subproblem 1
n + 2.944444445 = 2.976613727

Simplifying
n + 2.944444445 = 2.976613727

Reorder the terms:
2.944444445 + n = 2.976613727

Solving
2.944444445 + n = 2.976613727

Solving for variable 'n'.

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

Add '-2.944444445' to each side of the equation.
2.944444445 + -2.944444445 + n = 2.976613727 + -2.944444445

Combine like terms: 2.944444445 + -2.944444445 = 0.000000000
0.000000000 + n = 2.976613727 + -2.944444445
n = 2.976613727 + -2.944444445

Combine like terms: 2.976613727 + -2.944444445 = 0.032169282
n = 0.032169282

Simplifying
n = 0.032169282

Subproblem 2
n + 2.944444445 = -2.976613727

Simplifying
n + 2.944444445 = -2.976613727

Reorder the terms:
2.944444445 + n = -2.976613727

Solving
2.944444445 + n = -2.976613727

Solving for variable 'n'.

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

Add '-2.944444445' to each side of the equation.
2.944444445 + -2.944444445 + n = -2.976613727 + -2.944444445

Combine like terms: 2.944444445 + -2.944444445 = 0.000000000
0.000000000 + n = -2.976613727 + -2.944444445
n = -2.976613727 + -2.944444445

Combine like terms: -2.976613727 + -2.944444445 = -5.921058172
n = -5.921058172

Simplifying
n = -5.921058172

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.032169282, -5.921058172}
Solution
n = {0.032169282, -5.921058172}