(2x+4)(x-6)=8

Solution for (2x+4)(x-6)=8 equation:

Simplifying
(2x + 4)(x + -6) = 8

Reorder the terms:
(4 + 2x)(x + -6) = 8

Reorder the terms:
(4 + 2x)(-6 + x) = 8

Multiply (4 + 2x) * (-6 + x)
(4(-6 + x) + 2x * (-6 + x)) = 8
((-6 * 4 + x * 4) + 2x * (-6 + x)) = 8
((-24 + 4x) + 2x * (-6 + x)) = 8
(-24 + 4x + (-6 * 2x + x * 2x)) = 8
(-24 + 4x + (-12x + 2x2)) = 8

Combine like terms: 4x + -12x = -8x
(-24 + -8x + 2x2) = 8

Solving
-24 + -8x + 2x2 = 8

Solving for variable 'x'.

Reorder the terms:
-24 + -8 + -8x + 2x2 = 8 + -8

Combine like terms: -24 + -8 = -32
-32 + -8x + 2x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-32 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -4x + x2 = 0

Solving
-16 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -4x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -4x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -4x + x2 = 0 + 16
-4x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-4x + x2 = 16

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 = 16 + 4

Reorder the terms:
4 + -4x + x2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + -4x + x2 = 20

Factor a perfect square on the left side:
(x + -2)(x + -2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -2) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + -2 = 4.472135955

Simplifying
x + -2 = 4.472135955

Reorder the terms:
-2 + x = 4.472135955

Solving
-2 + x = 4.472135955

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 = 4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.472135955 + 2
x = 4.472135955 + 2

Combine like terms: 4.472135955 + 2 = 6.472135955
x = 6.472135955

Simplifying
x = 6.472135955

Subproblem 2
x + -2 = -4.472135955

Simplifying
x + -2 = -4.472135955

Reorder the terms:
-2 + x = -4.472135955

Solving
-2 + x = -4.472135955

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 = -4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.472135955 + 2
x = -4.472135955 + 2

Combine like terms: -4.472135955 + 2 = -2.472135955
x = -2.472135955

Simplifying
x = -2.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.472135955, -2.472135955}
Solution
x = {6.472135955, -2.472135955}