6n^2+64n+56=2n^2

Solution for 6n^2+64n+56=2n^2 equation:

Simplifying
6n2 + 64n + 56 = 2n2

Reorder the terms:
56 + 64n + 6n2 = 2n2

Solving
56 + 64n + 6n2 = 2n2

Solving for variable 'n'.

Combine like terms: 6n2 + -2n2 = 4n2
56 + 64n + 4n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
56 + 64n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + 16n + n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(14 + 16n + n2)' equal to zero and attempt to solve:

Simplifying
14 + 16n + n2 = 0

Solving
14 + 16n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 16n + -14 + n2 = 0 + -14

Reorder the terms:
14 + -14 + 16n + n2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 16n + n2 = 0 + -14
16n + n2 = 0 + -14

Combine like terms: 0 + -14 = -14
16n + n2 = -14

The n term is 16n.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16n + 64 + n2 = -14 + 64

Reorder the terms:
64 + 16n + n2 = -14 + 64

Combine like terms: -14 + 64 = 50
64 + 16n + n2 = 50

Factor a perfect square on the left side:
(n + 8)(n + 8) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(n + 8) equal to 7.071067812 and -7.071067812.

Subproblem 1
n + 8 = 7.071067812

Simplifying
n + 8 = 7.071067812

Reorder the terms:
8 + n = 7.071067812

Solving
8 + n = 7.071067812

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = 7.071067812 + -8

Combine like terms: 8 + -8 = 0
0 + n = 7.071067812 + -8
n = 7.071067812 + -8

Combine like terms: 7.071067812 + -8 = -0.928932188
n = -0.928932188

Simplifying
n = -0.928932188

Subproblem 2
n + 8 = -7.071067812

Simplifying
n + 8 = -7.071067812

Reorder the terms:
8 + n = -7.071067812

Solving
8 + n = -7.071067812

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = -7.071067812 + -8

Combine like terms: 8 + -8 = 0
0 + n = -7.071067812 + -8
n = -7.071067812 + -8

Combine like terms: -7.071067812 + -8 = -15.071067812
n = -15.071067812

Simplifying
n = -15.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.928932188, -15.071067812}
Solution
n = {-0.928932188, -15.071067812}