n^2+6n-20=0

Solution for n^2+6n-20=0 equation:

Simplifying
n2 + 6n + -20 = 0

Reorder the terms:
-20 + 6n + n2 = 0

Solving
-20 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 6n + 20 + n2 = 0 + 20

Reorder the terms:
-20 + 20 + 6n + n2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 6n + n2 = 0 + 20
6n + n2 = 0 + 20

Combine like terms: 0 + 20 = 20
6n + n2 = 20

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = 20 + 9

Reorder the terms:
9 + 6n + n2 = 20 + 9

Combine like terms: 20 + 9 = 29
9 + 6n + n2 = 29

Factor a perfect square on the left side:
(n + 3)(n + 3) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(n + 3) equal to 5.385164807 and -5.385164807.

Subproblem 1
n + 3 = 5.385164807

Simplifying
n + 3 = 5.385164807

Reorder the terms:
3 + n = 5.385164807

Solving
3 + n = 5.385164807

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = 5.385164807 + -3

Combine like terms: 3 + -3 = 0
0 + n = 5.385164807 + -3
n = 5.385164807 + -3

Combine like terms: 5.385164807 + -3 = 2.385164807
n = 2.385164807

Simplifying
n = 2.385164807

Subproblem 2
n + 3 = -5.385164807

Simplifying
n + 3 = -5.385164807

Reorder the terms:
3 + n = -5.385164807

Solving
3 + n = -5.385164807

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = -5.385164807 + -3

Combine like terms: 3 + -3 = 0
0 + n = -5.385164807 + -3
n = -5.385164807 + -3

Combine like terms: -5.385164807 + -3 = -8.385164807
n = -8.385164807

Simplifying
n = -8.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.385164807, -8.385164807}