120n(2)14n-8=2n

Solution for 120n(2)14n-8=2n equation:

Simplifying
120n(2) * 14n + -8 = 2n

Reorder the terms for easier multiplication:
120 * 2 * 14n * n + -8 = 2n

Multiply 120 * 2
240 * 14n * n + -8 = 2n

Multiply 240 * 14
3360n * n + -8 = 2n

Multiply n * n
3360n2 + -8 = 2n

Reorder the terms:
-8 + 3360n2 = 2n

Solving
-8 + 3360n2 = 2n

Solving for variable 'n'.

Reorder the terms:
-8 + -2n + 3360n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-8 + -2n + 3360n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -1n + 1680n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1n + 1680n2)' equal to zero and attempt to solve:

Simplifying
-4 + -1n + 1680n2 = 0

Solving
-4 + -1n + 1680n2 = 0

Begin completing the square.  Divide all terms by
1680 the coefficient of the squared term: 

Divide each side by '1680'.
-0.002380952381 + -0.0005952380952n + n2 = 0.0

Move the constant term to the right:

Add '0.002380952381' to each side of the equation.
-0.002380952381 + -0.0005952380952n + 0.002380952381 + n2 = 0.0 + 0.002380952381

Reorder the terms:
-0.002380952381 + 0.002380952381 + -0.0005952380952n + n2 = 0.0 + 0.002380952381

Combine like terms: -0.002380952381 + 0.002380952381 = 0.000000000000
0.000000000000 + -0.0005952380952n + n2 = 0.0 + 0.002380952381
-0.0005952380952n + n2 = 0.0 + 0.002380952381

Combine like terms: 0.0 + 0.002380952381 = 0.002380952381
-0.0005952380952n + n2 = 0.002380952381

The n term is -0.0005952380952n.  Take half its coefficient (-0.0002976190476).
Square it (0.00000008857709749) and add it to both sides.

Add '0.00000008857709749' to each side of the equation.
-0.0005952380952n + 0.00000008857709749 + n2 = 0.002380952381 + 0.00000008857709749

Reorder the terms:
0.00000008857709749 + -0.0005952380952n + n2 = 0.002380952381 + 0.00000008857709749

Combine like terms: 0.002380952381 + 0.00000008857709749 = 0.00238104095809749
0.00000008857709749 + -0.0005952380952n + n2 = 0.00238104095809749

Factor a perfect square on the left side:
(n + -0.0002976190476)(n + -0.0002976190476) = 0.00238104095809749

Calculate the square root of the right side: 0.048795911

Break this problem into two subproblems by setting 
(n + -0.0002976190476) equal to 0.048795911 and -0.048795911.

Subproblem 1
n + -0.0002976190476 = 0.048795911

Simplifying
n + -0.0002976190476 = 0.048795911

Reorder the terms:
-0.0002976190476 + n = 0.048795911

Solving
-0.0002976190476 + n = 0.048795911

Solving for variable 'n'.

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

Add '0.0002976190476' to each side of the equation.
-0.0002976190476 + 0.0002976190476 + n = 0.048795911 + 0.0002976190476

Combine like terms: -0.0002976190476 + 0.0002976190476 = 0.0000000000000
0.0000000000000 + n = 0.048795911 + 0.0002976190476
n = 0.048795911 + 0.0002976190476

Combine like terms: 0.048795911 + 0.0002976190476 = 0.0490935300476
n = 0.0490935300476

Simplifying
n = 0.0490935300476

Subproblem 2
n + -0.0002976190476 = -0.048795911

Simplifying
n + -0.0002976190476 = -0.048795911

Reorder the terms:
-0.0002976190476 + n = -0.048795911

Solving
-0.0002976190476 + n = -0.048795911

Solving for variable 'n'.

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

Add '0.0002976190476' to each side of the equation.
-0.0002976190476 + 0.0002976190476 + n = -0.048795911 + 0.0002976190476

Combine like terms: -0.0002976190476 + 0.0002976190476 = 0.0000000000000
0.0000000000000 + n = -0.048795911 + 0.0002976190476
n = -0.048795911 + 0.0002976190476

Combine like terms: -0.048795911 + 0.0002976190476 = -0.0484982919524
n = -0.0484982919524

Simplifying
n = -0.0484982919524

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.0490935300476, -0.0484982919524}
Solution
n = {0.0490935300476, -0.0484982919524}