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

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

Simplifying
(x + 6)(x + -4) + (x + 2)(x + -2) = 0

Reorder the terms:
(6 + x)(x + -4) + (x + 2)(x + -2) = 0

Reorder the terms:
(6 + x)(-4 + x) + (x + 2)(x + -2) = 0

Multiply (6 + x) * (-4 + x)
(6(-4 + x) + x(-4 + x)) + (x + 2)(x + -2) = 0
((-4 * 6 + x * 6) + x(-4 + x)) + (x + 2)(x + -2) = 0
((-24 + 6x) + x(-4 + x)) + (x + 2)(x + -2) = 0
(-24 + 6x + (-4 * x + x * x)) + (x + 2)(x + -2) = 0
(-24 + 6x + (-4x + x2)) + (x + 2)(x + -2) = 0

Combine like terms: 6x + -4x = 2x
(-24 + 2x + x2) + (x + 2)(x + -2) = 0

Reorder the terms:
-24 + 2x + x2 + (2 + x)(x + -2) = 0

Reorder the terms:
-24 + 2x + x2 + (2 + x)(-2 + x) = 0

Multiply (2 + x) * (-2 + x)
-24 + 2x + x2 + (2(-2 + x) + x(-2 + x)) = 0
-24 + 2x + x2 + ((-2 * 2 + x * 2) + x(-2 + x)) = 0
-24 + 2x + x2 + ((-4 + 2x) + x(-2 + x)) = 0
-24 + 2x + x2 + (-4 + 2x + (-2 * x + x * x)) = 0
-24 + 2x + x2 + (-4 + 2x + (-2x + x2)) = 0

Combine like terms: 2x + -2x = 0
-24 + 2x + x2 + (-4 + 0 + x2) = 0
-24 + 2x + x2 + (-4 + x2) = 0

Reorder the terms:
-24 + -4 + 2x + x2 + x2 = 0

Combine like terms: -24 + -4 = -28
-28 + 2x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-28 + 2x + 2x2 = 0

Solving
-28 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + x + x2 = 0

Solving
-14 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x + x2 = 0 + 14
x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
x + x2 = 14

The x term is x.  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.
x + 0.25 + x2 = 14 + 0.25

Reorder the terms:
0.25 + x + x2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + x + x2 = 14.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + 0.5 = 3.774917218

Simplifying
x + 0.5 = 3.774917218

Reorder the terms:
0.5 + x = 3.774917218

Solving
0.5 + x = 3.774917218

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 = 3.774917218 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.774917218 + -0.5
x = 3.774917218 + -0.5

Combine like terms: 3.774917218 + -0.5 = 3.274917218
x = 3.274917218

Simplifying
x = 3.274917218

Subproblem 2
x + 0.5 = -3.774917218

Simplifying
x + 0.5 = -3.774917218

Reorder the terms:
0.5 + x = -3.774917218

Solving
0.5 + x = -3.774917218

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 = -3.774917218 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.774917218 + -0.5
x = -3.774917218 + -0.5

Combine like terms: -3.774917218 + -0.5 = -4.274917218
x = -4.274917218

Simplifying
x = -4.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.274917218, -4.274917218}
Solution
x = {3.274917218, -4.274917218}