14n^2-36n-60=0

Solution for 14n^2-36n-60=0 equation:

Simplifying
14n2 + -36n + -60 = 0

Reorder the terms:
-60 + -36n + 14n2 = 0

Solving
-60 + -36n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -18n + 7n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + -18n + 7n2)' equal to zero and attempt to solve:

Simplifying
-30 + -18n + 7n2 = 0

Solving
-30 + -18n + 7n2 = 0

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

Divide each side by '7'.
-4.285714286 + -2.571428571n + n2 = 0

Move the constant term to the right:

Add '4.285714286' to each side of the equation.
-4.285714286 + -2.571428571n + 4.285714286 + n2 = 0 + 4.285714286

Reorder the terms:
-4.285714286 + 4.285714286 + -2.571428571n + n2 = 0 + 4.285714286

Combine like terms: -4.285714286 + 4.285714286 = 0.000000000
0.000000000 + -2.571428571n + n2 = 0 + 4.285714286
-2.571428571n + n2 = 0 + 4.285714286

Combine like terms: 0 + 4.285714286 = 4.285714286
-2.571428571n + n2 = 4.285714286

The n term is -2.571428571n.  Take half its coefficient (-1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
-2.571428571n + 1.653061225 + n2 = 4.285714286 + 1.653061225

Reorder the terms:
1.653061225 + -2.571428571n + n2 = 4.285714286 + 1.653061225

Combine like terms: 4.285714286 + 1.653061225 = 5.938775511
1.653061225 + -2.571428571n + n2 = 5.938775511

Factor a perfect square on the left side:
(n + -1.285714286)(n + -1.285714286) = 5.938775511

Calculate the square root of the right side: 2.436960301

Break this problem into two subproblems by setting 
(n + -1.285714286) equal to 2.436960301 and -2.436960301.

Subproblem 1
n + -1.285714286 = 2.436960301

Simplifying
n + -1.285714286 = 2.436960301

Reorder the terms:
-1.285714286 + n = 2.436960301

Solving
-1.285714286 + n = 2.436960301

Solving for variable 'n'.

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

Add '1.285714286' to each side of the equation.
-1.285714286 + 1.285714286 + n = 2.436960301 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + n = 2.436960301 + 1.285714286
n = 2.436960301 + 1.285714286

Combine like terms: 2.436960301 + 1.285714286 = 3.722674587
n = 3.722674587

Simplifying
n = 3.722674587

Subproblem 2
n + -1.285714286 = -2.436960301

Simplifying
n + -1.285714286 = -2.436960301

Reorder the terms:
-1.285714286 + n = -2.436960301

Solving
-1.285714286 + n = -2.436960301

Solving for variable 'n'.

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

Add '1.285714286' to each side of the equation.
-1.285714286 + 1.285714286 + n = -2.436960301 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + n = -2.436960301 + 1.285714286
n = -2.436960301 + 1.285714286

Combine like terms: -2.436960301 + 1.285714286 = -1.151246015
n = -1.151246015

Simplifying
n = -1.151246015

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.722674587, -1.151246015}
Solution
n = {3.722674587, -1.151246015}