-10n^2+10n+3636=0

Solution for -10n^2+10n+3636=0 equation:

Simplifying
-10n2 + 10n + 3636 = 0

Reorder the terms:
3636 + 10n + -10n2 = 0

Solving
3636 + 10n + -10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1818 + 5n + -5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1818 + 5n + -5n2)' equal to zero and attempt to solve:

Simplifying
1818 + 5n + -5n2 = 0

Solving
1818 + 5n + -5n2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-363.6 + -1n + n2 = 0

Move the constant term to the right:

Add '363.6' to each side of the equation.
-363.6 + -1n + 363.6 + n2 = 0 + 363.6

Reorder the terms:
-363.6 + 363.6 + -1n + n2 = 0 + 363.6

Combine like terms: -363.6 + 363.6 = 0.0
0.0 + -1n + n2 = 0 + 363.6
-1n + n2 = 0 + 363.6

Combine like terms: 0 + 363.6 = 363.6
-1n + n2 = 363.6

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 = 363.6 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 363.6 + 0.25

Combine like terms: 363.6 + 0.25 = 363.85
0.25 + -1n + n2 = 363.85

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 363.85

Calculate the square root of the right side: 19.074852555

Break this problem into two subproblems by setting 
(n + -0.5) equal to 19.074852555 and -19.074852555.

Subproblem 1
n + -0.5 = 19.074852555

Simplifying
n + -0.5 = 19.074852555

Reorder the terms:
-0.5 + n = 19.074852555

Solving
-0.5 + n = 19.074852555

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 = 19.074852555 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 19.074852555 + 0.5
n = 19.074852555 + 0.5

Combine like terms: 19.074852555 + 0.5 = 19.574852555
n = 19.574852555

Simplifying
n = 19.574852555

Subproblem 2
n + -0.5 = -19.074852555

Simplifying
n + -0.5 = -19.074852555

Reorder the terms:
-0.5 + n = -19.074852555

Solving
-0.5 + n = -19.074852555

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 = -19.074852555 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -19.074852555 + 0.5
n = -19.074852555 + 0.5

Combine like terms: -19.074852555 + 0.5 = -18.574852555
n = -18.574852555

Simplifying
n = -18.574852555

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {19.574852555, -18.574852555}
Solution
n = {19.574852555, -18.574852555}