(x-2)(x+6)=8

Solution for (x-2)(x+6)=8 equation:

Simplifying
(x + -2)(x + 6) = 8

Reorder the terms:
(-2 + x)(x + 6) = 8

Reorder the terms:
(-2 + x)(6 + x) = 8

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) = 8
((6 * -2 + x * -2) + x(6 + x)) = 8
((-12 + -2x) + x(6 + x)) = 8
(-12 + -2x + (6 * x + x * x)) = 8
(-12 + -2x + (6x + x2)) = 8

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = 8

Solving
-12 + 4x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-12 + -8 + 4x + x2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + 4x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 4x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 4x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 4x + x2 = 0 + 20
4x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
4x + x2 = 20

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 = 20 + 4

Reorder the terms:
4 + 4x + x2 = 20 + 4

Combine like terms: 20 + 4 = 24
4 + 4x + x2 = 24

Factor a perfect square on the left side:
(x + 2)(x + 2) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 2) equal to 4.898979486 and -4.898979486.

Subproblem 1
x + 2 = 4.898979486

Simplifying
x + 2 = 4.898979486

Reorder the terms:
2 + x = 4.898979486

Solving
2 + x = 4.898979486

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 = 4.898979486 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.898979486 + -2
x = 4.898979486 + -2

Combine like terms: 4.898979486 + -2 = 2.898979486
x = 2.898979486

Simplifying
x = 2.898979486

Subproblem 2
x + 2 = -4.898979486

Simplifying
x + 2 = -4.898979486

Reorder the terms:
2 + x = -4.898979486

Solving
2 + x = -4.898979486

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 = -4.898979486 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.898979486 + -2
x = -4.898979486 + -2

Combine like terms: -4.898979486 + -2 = -6.898979486
x = -6.898979486

Simplifying
x = -6.898979486

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.898979486, -6.898979486}