2n(2n-20)=2

Solution for 2n(2n-20)=2 equation:

Simplifying
2n(2n + -20) = 2

Reorder the terms:
2n(-20 + 2n) = 2
(-20 * 2n + 2n * 2n) = 2
(-40n + 4n2) = 2

Solving
-40n + 4n2 = 2

Solving for variable 'n'.

Reorder the terms:
-2 + -40n + 4n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -40n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -20n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -20n + 2n2)' equal to zero and attempt to solve:

Simplifying
-1 + -20n + 2n2 = 0

Solving
-1 + -20n + 2n2 = 0

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

Divide each side by '2'.
-0.5 + -10n + n2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -10n + 0.5 + n2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -10n + n2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -10n + n2 = 0 + 0.5
-10n + n2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-10n + n2 = 0.5

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = 0.5 + 25

Reorder the terms:
25 + -10n + n2 = 0.5 + 25

Combine like terms: 0.5 + 25 = 25.5
25 + -10n + n2 = 25.5

Factor a perfect square on the left side:
(n + -5)(n + -5) = 25.5

Calculate the square root of the right side: 5.049752469

Break this problem into two subproblems by setting 
(n + -5) equal to 5.049752469 and -5.049752469.

Subproblem 1
n + -5 = 5.049752469

Simplifying
n + -5 = 5.049752469

Reorder the terms:
-5 + n = 5.049752469

Solving
-5 + n = 5.049752469

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = 5.049752469 + 5

Combine like terms: -5 + 5 = 0
0 + n = 5.049752469 + 5
n = 5.049752469 + 5

Combine like terms: 5.049752469 + 5 = 10.049752469
n = 10.049752469

Simplifying
n = 10.049752469

Subproblem 2
n + -5 = -5.049752469

Simplifying
n + -5 = -5.049752469

Reorder the terms:
-5 + n = -5.049752469

Solving
-5 + n = -5.049752469

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = -5.049752469 + 5

Combine like terms: -5 + 5 = 0
0 + n = -5.049752469 + 5
n = -5.049752469 + 5

Combine like terms: -5.049752469 + 5 = -0.049752469
n = -0.049752469

Simplifying
n = -0.049752469

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.049752469, -0.049752469}
Solution
n = {10.049752469, -0.049752469}