(n+5)*(n-6)=72

Solution for (n+5)*(n-6)=72 equation:

Simplifying
(n + 5)(n + -6) = 72

Reorder the terms:
(5 + n)(n + -6) = 72

Reorder the terms:
(5 + n)(-6 + n) = 72

Multiply (5 + n) * (-6 + n)
(5(-6 + n) + n(-6 + n)) = 72
((-6 * 5 + n * 5) + n(-6 + n)) = 72
((-30 + 5n) + n(-6 + n)) = 72
(-30 + 5n + (-6 * n + n * n)) = 72
(-30 + 5n + (-6n + n2)) = 72

Combine like terms: 5n + -6n = -1n
(-30 + -1n + n2) = 72

Solving
-30 + -1n + n2 = 72

Solving for variable 'n'.

Reorder the terms:
-30 + -72 + -1n + n2 = 72 + -72

Combine like terms: -30 + -72 = -102
-102 + -1n + n2 = 72 + -72

Combine like terms: 72 + -72 = 0
-102 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + -1n + 102 + n2 = 0 + 102

Reorder the terms:
-102 + 102 + -1n + n2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -1n + n2 = 0 + 102
-1n + n2 = 0 + 102

Combine like terms: 0 + 102 = 102
-1n + n2 = 102

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 = 102 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 102 + 0.25

Combine like terms: 102 + 0.25 = 102.25
0.25 + -1n + n2 = 102.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(n + -0.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
n + -0.5 = 10.111874208

Simplifying
n + -0.5 = 10.111874208

Reorder the terms:
-0.5 + n = 10.111874208

Solving
-0.5 + n = 10.111874208

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 = 10.111874208 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 10.111874208 + 0.5
n = 10.111874208 + 0.5

Combine like terms: 10.111874208 + 0.5 = 10.611874208
n = 10.611874208

Simplifying
n = 10.611874208

Subproblem 2
n + -0.5 = -10.111874208

Simplifying
n + -0.5 = -10.111874208

Reorder the terms:
-0.5 + n = -10.111874208

Solving
-0.5 + n = -10.111874208

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 = -10.111874208 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -10.111874208 + 0.5
n = -10.111874208 + 0.5

Combine like terms: -10.111874208 + 0.5 = -9.611874208
n = -9.611874208

Simplifying
n = -9.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.611874208, -9.611874208}