(x+6)(x+9)=16

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Solution for (x+6)(x+9)=16 equation: 


Simplifying
(x + 6)(x + 9) = 16

Reorder the terms:
(6 + x)(x + 9) = 16

Reorder the terms:
(6 + x)(9 + x) = 16

Multiply (6 + x) * (9 + x)
(6(9 + x) + x(9 + x)) = 16
((9 * 6 + x * 6) + x(9 + x)) = 16
((54 + 6x) + x(9 + x)) = 16
(54 + 6x + (9 * x + x * x)) = 16
(54 + 6x + (9x + x2)) = 16

Combine like terms: 6x + 9x = 15x
(54 + 15x + x2) = 16

Solving
54 + 15x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
54 + -16 + 15x + x2 = 16 + -16

Combine like terms: 54 + -16 = 38
38 + 15x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
38 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + 15x + -38 + x2 = 0 + -38

Reorder the terms:
38 + -38 + 15x + x2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 15x + x2 = 0 + -38
15x + x2 = 0 + -38

Combine like terms: 0 + -38 = -38
15x + x2 = -38

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -38 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -38 + 56.25

Combine like terms: -38 + 56.25 = 18.25
56.25 + 15x + x2 = 18.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 7.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 7.5 = 4.272001873

Simplifying
x + 7.5 = 4.272001873

Reorder the terms:
7.5 + x = 4.272001873

Solving
7.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 4.272001873 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 4.272001873 + -7.5
x = 4.272001873 + -7.5

Combine like terms: 4.272001873 + -7.5 = -3.227998127
x = -3.227998127

Simplifying
x = -3.227998127


Subproblem 2
x + 7.5 = -4.272001873

Simplifying
x + 7.5 = -4.272001873

Reorder the terms:
7.5 + x = -4.272001873

Solving
7.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -4.272001873 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -4.272001873 + -7.5
x = -4.272001873 + -7.5

Combine like terms: -4.272001873 + -7.5 = -11.772001873
x = -11.772001873

Simplifying
x = -11.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.227998127, -11.772001873}

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