2n^2-2n-20=0

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

Simplifying
2n2 + -2n + -20 = 0

Reorder the terms:
-20 + -2n + 2n2 = 0

Solving
-20 + -2n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1n + n2)' equal to zero and attempt to solve:

Simplifying
-10 + -1n + n2 = 0

Solving
-10 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -1n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + -1n + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n + n2 = 0 + 10
-1n + n2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1n + n2 = 10

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 10 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + -1n + n2 = 10.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(n + -0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
n + -0.5 = 3.201562119

Simplifying
n + -0.5 = 3.201562119

Reorder the terms:
-0.5 + n = 3.201562119

Solving
-0.5 + n = 3.201562119

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 3.201562119 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 3.201562119 + 0.5
n = 3.201562119 + 0.5

Combine like terms: 3.201562119 + 0.5 = 3.701562119
n = 3.701562119

Simplifying
n = 3.701562119

Subproblem 2
n + -0.5 = -3.201562119

Simplifying
n + -0.5 = -3.201562119

Reorder the terms:
-0.5 + n = -3.201562119

Solving
-0.5 + n = -3.201562119

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -3.201562119 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -3.201562119 + 0.5
n = -3.201562119 + 0.5

Combine like terms: -3.201562119 + 0.5 = -2.701562119
n = -2.701562119

Simplifying
n = -2.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.701562119, -2.701562119}
Solution
n = {3.701562119, -2.701562119}