(n^2)+2n-6=0

Solution for (n^2)+2n-6=0 equation:

Simplifying
(n2) + 2n + -6 = 0
n2 + 2n + -6 = 0

Reorder the terms:
-6 + 2n + n2 = 0

Solving
-6 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + 2n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2n + n2 = 0 + 6
2n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
2n + n2 = 6

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 6 + 1

Reorder the terms:
1 + 2n + n2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2n + n2 = 7

Factor a perfect square on the left side:
(n + 1)(n + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
n + 1 = 2.645751311

Simplifying
n + 1 = 2.645751311

Reorder the terms:
1 + n = 2.645751311

Solving
1 + n = 2.645751311

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + n = 2.645751311 + -1
n = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
n = 1.645751311

Simplifying
n = 1.645751311

Subproblem 2
n + 1 = -2.645751311

Simplifying
n + 1 = -2.645751311

Reorder the terms:
1 + n = -2.645751311

Solving
1 + n = -2.645751311

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + n = -2.645751311 + -1
n = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
n = -3.645751311

Simplifying
n = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.645751311, -3.645751311}