36*n^2-630-72*n=0

Solution for 36*n^2-630-72*n=0 equation:

Simplifying
36n2 + -630 + -72n = 0

Reorder the terms:
-630 + -72n + 36n2 = 0

Solving
-630 + -72n + 36n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-35 + -4n + 2n2) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-35 + -4n + 2n2)' equal to zero and attempt to solve:

Simplifying
-35 + -4n + 2n2 = 0

Solving
-35 + -4n + 2n2 = 0

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

Divide each side by '2'.
-17.5 + -2n + n2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -2n + 17.5 + n2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -2n + n2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -2n + n2 = 0 + 17.5
-2n + n2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-2n + n2 = 17.5

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 = 17.5 + 1

Reorder the terms:
1 + -2n + n2 = 17.5 + 1

Combine like terms: 17.5 + 1 = 18.5
1 + -2n + n2 = 18.5

Factor a perfect square on the left side:
(n + -1)(n + -1) = 18.5

Calculate the square root of the right side: 4.301162634

Break this problem into two subproblems by setting 
(n + -1) equal to 4.301162634 and -4.301162634.

Subproblem 1
n + -1 = 4.301162634

Simplifying
n + -1 = 4.301162634

Reorder the terms:
-1 + n = 4.301162634

Solving
-1 + n = 4.301162634

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 = 4.301162634 + 1

Combine like terms: -1 + 1 = 0
0 + n = 4.301162634 + 1
n = 4.301162634 + 1

Combine like terms: 4.301162634 + 1 = 5.301162634
n = 5.301162634

Simplifying
n = 5.301162634

Subproblem 2
n + -1 = -4.301162634

Simplifying
n + -1 = -4.301162634

Reorder the terms:
-1 + n = -4.301162634

Solving
-1 + n = -4.301162634

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 = -4.301162634 + 1

Combine like terms: -1 + 1 = 0
0 + n = -4.301162634 + 1
n = -4.301162634 + 1

Combine like terms: -4.301162634 + 1 = -3.301162634
n = -3.301162634

Simplifying
n = -3.301162634

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.301162634, -3.301162634}
Solution
n = {5.301162634, -3.301162634}