(x-5)(x+6)=72

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

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

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

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

Multiply (-5 + x) * (6 + x)
(-5(6 + x) + x(6 + x)) = 72
((6 * -5 + x * -5) + x(6 + x)) = 72
((-30 + -5x) + x(6 + x)) = 72
(-30 + -5x + (6 * x + x * x)) = 72
(-30 + -5x + (6x + x2)) = 72

Combine like terms: -5x + 6x = 1x
(-30 + 1x + x2) = 72

Solving
-30 + 1x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
-30 + -72 + 1x + x2 = 72 + -72

Combine like terms: -30 + -72 = -102
-102 + 1x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-102 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 1x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 1x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 1x + x2 = 0 + 102
1x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
1x + x2 = 102

The x term is 1x.  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.
x + 0.25 + x2 = 102 + 0.25

Reorder the terms:
0.25 + x + x2 = 102 + 0.25

Combine like terms: 102 + 0.25 = 102.25
0.25 + x + x2 = 102.25

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

Calculate the square root of the right side: 10.111874208

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

Subproblem 1
x + 0.5 = 10.111874208

Simplifying
x + 0.5 = 10.111874208

Reorder the terms:
0.5 + x = 10.111874208

Solving
0.5 + x = 10.111874208

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 10.111874208 + -0.5

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

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

Simplifying
x = 9.611874208

Subproblem 2
x + 0.5 = -10.111874208

Simplifying
x + 0.5 = -10.111874208

Reorder the terms:
0.5 + x = -10.111874208

Solving
0.5 + x = -10.111874208

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -10.111874208 + -0.5

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

Combine like terms: -10.111874208 + -0.5 = -10.611874208
x = -10.611874208

Simplifying
x = -10.611874208

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