2(n^2+2n-72)=0

Solution for 2(n^2+2n-72)=0 equation:

Simplifying
2(n2 + 2n + -72) = 0

Reorder the terms:
2(-72 + 2n + n2) = 0
(-72 * 2 + 2n * 2 + n2 * 2) = 0
(-144 + 4n + 2n2) = 0

Solving
-144 + 4n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + 2n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-72 + 2n + n2)' equal to zero and attempt to solve:

Simplifying
-72 + 2n + n2 = 0

Solving
-72 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 2n + 72 + n2 = 0 + 72

Reorder the terms:
-72 + 72 + 2n + n2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 2n + n2 = 0 + 72
2n + n2 = 0 + 72

Combine like terms: 0 + 72 = 72
2n + n2 = 72

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 = 72 + 1

Reorder the terms:
1 + 2n + n2 = 72 + 1

Combine like terms: 72 + 1 = 73
1 + 2n + n2 = 73

Factor a perfect square on the left side:
(n + 1)(n + 1) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(n + 1) equal to 8.544003745 and -8.544003745.

Subproblem 1
n + 1 = 8.544003745

Simplifying
n + 1 = 8.544003745

Reorder the terms:
1 + n = 8.544003745

Solving
1 + n = 8.544003745

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 = 8.544003745 + -1

Combine like terms: 1 + -1 = 0
0 + n = 8.544003745 + -1
n = 8.544003745 + -1

Combine like terms: 8.544003745 + -1 = 7.544003745
n = 7.544003745

Simplifying
n = 7.544003745

Subproblem 2
n + 1 = -8.544003745

Simplifying
n + 1 = -8.544003745

Reorder the terms:
1 + n = -8.544003745

Solving
1 + n = -8.544003745

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 = -8.544003745 + -1

Combine like terms: 1 + -1 = 0
0 + n = -8.544003745 + -1
n = -8.544003745 + -1

Combine like terms: -8.544003745 + -1 = -9.544003745
n = -9.544003745

Simplifying
n = -9.544003745

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.544003745, -9.544003745}
Solution
n = {7.544003745, -9.544003745}