n=(n^2+4n-6)+(n-2)

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Solution for n=(n^2+4n-6)+(n-2) equation: 


Simplifying
n = (n2 + 4n + -6) + (n + -2)

Reorder the terms:
n = (-6 + 4n + n2) + (n + -2)

Remove parenthesis around (-6 + 4n + n2)
n = -6 + 4n + n2 + (n + -2)

Reorder the terms:
n = -6 + 4n + n2 + (-2 + n)

Remove parenthesis around (-2 + n)
n = -6 + 4n + n2 + -2 + n

Reorder the terms:
n = -6 + -2 + 4n + n + n2

Combine like terms: -6 + -2 = -8
n = -8 + 4n + n + n2

Combine like terms: 4n + n = 5n
n = -8 + 5n + n2

Solving
n = -8 + 5n + n2

Solving for variable 'n'.

Reorder the terms:
8 + n + -5n + -1n2 = -8 + 5n + n2 + 8 + -5n + -1n2

Combine like terms: n + -5n = -4n
8 + -4n + -1n2 = -8 + 5n + n2 + 8 + -5n + -1n2

Reorder the terms:
8 + -4n + -1n2 = -8 + 8 + 5n + -5n + n2 + -1n2

Combine like terms: -8 + 8 = 0
8 + -4n + -1n2 = 0 + 5n + -5n + n2 + -1n2
8 + -4n + -1n2 = 5n + -5n + n2 + -1n2

Combine like terms: 5n + -5n = 0
8 + -4n + -1n2 = 0 + n2 + -1n2
8 + -4n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
8 + -4n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + 4n + n2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4n + 8 + n2 = 0 + 8

Reorder the terms:
-8 + 8 + 4n + n2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 4n + n2 = 0 + 8
4n + n2 = 0 + 8

Combine like terms: 0 + 8 = 8
4n + n2 = 8

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 8 + 4

Reorder the terms:
4 + 4n + n2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + 4n + n2 = 12

Factor a perfect square on the left side:
(n + 2)(n + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(n + 2) equal to 3.464101615 and -3.464101615.


Subproblem 1
n + 2 = 3.464101615

Simplifying
n + 2 = 3.464101615

Reorder the terms:
2 + n = 3.464101615

Solving
2 + n = 3.464101615

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = 3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + n = 3.464101615 + -2
n = 3.464101615 + -2

Combine like terms: 3.464101615 + -2 = 1.464101615
n = 1.464101615

Simplifying
n = 1.464101615


Subproblem 2
n + 2 = -3.464101615

Simplifying
n + 2 = -3.464101615

Reorder the terms:
2 + n = -3.464101615

Solving
2 + n = -3.464101615

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = -3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + n = -3.464101615 + -2
n = -3.464101615 + -2

Combine like terms: -3.464101615 + -2 = -5.464101615
n = -5.464101615

Simplifying
n = -5.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.464101615, -5.464101615}

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