(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.
-1x + 0.25 + x2 = 102 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 102 + 0.25

Combine like terms: 102 + 0.25 = 102.25
0.25 + -1x + 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 = 10.611874208
x = 10.611874208

Simplifying
x = 10.611874208

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 = -9.611874208
x = -9.611874208

Simplifying
x = -9.611874208

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