(x+2)*(x-6)-6=0

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Solution for (x+2)*(x-6)-6=0 equation: 


Simplifying
(x + 2)(x + -6) + -6 = 0

Reorder the terms:
(2 + x)(x + -6) + -6 = 0

Reorder the terms:
(2 + x)(-6 + x) + -6 = 0

Multiply (2 + x) * (-6 + x)
(2(-6 + x) + x(-6 + x)) + -6 = 0
((-6 * 2 + x * 2) + x(-6 + x)) + -6 = 0
((-12 + 2x) + x(-6 + x)) + -6 = 0
(-12 + 2x + (-6 * x + x * x)) + -6 = 0
(-12 + 2x + (-6x + x2)) + -6 = 0

Combine like terms: 2x + -6x = -4x
(-12 + -4x + x2) + -6 = 0

Reorder the terms:
-12 + -6 + -4x + x2 = 0

Combine like terms: -12 + -6 = -18
-18 + -4x + x2 = 0

Solving
-18 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -4x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -4x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -4x + x2 = 0 + 18
-4x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-4x + x2 = 18

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 18 + 4

Reorder the terms:
4 + -4x + x2 = 18 + 4

Combine like terms: 18 + 4 = 22
4 + -4x + x2 = 22

Factor a perfect square on the left side:
(x + -2)(x + -2) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -2) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + -2 = 4.69041576

Simplifying
x + -2 = 4.69041576

Reorder the terms:
-2 + x = 4.69041576

Solving
-2 + x = 4.69041576

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.69041576 + 2
x = 4.69041576 + 2

Combine like terms: 4.69041576 + 2 = 6.69041576
x = 6.69041576

Simplifying
x = 6.69041576


Subproblem 2
x + -2 = -4.69041576

Simplifying
x + -2 = -4.69041576

Reorder the terms:
-2 + x = -4.69041576

Solving
-2 + x = -4.69041576

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.69041576 + 2
x = -4.69041576 + 2

Combine like terms: -4.69041576 + 2 = -2.69041576
x = -2.69041576

Simplifying
x = -2.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.69041576, -2.69041576}

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