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

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Solution for (x+6)(x+6)-(x-6)(x-6)-(x-4)(x-4)=0 equation: 


Simplifying
(x + 6)(x + 6) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0

Reorder the terms:
(6 + x)(x + 6) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0

Reorder the terms:
(6 + x)(6 + x) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0
((6 * 6 + x * 6) + x(6 + x)) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0
((36 + 6x) + x(6 + x)) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0
(36 + 6x + (6 * x + x * x)) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0
(36 + 6x + (6x + x2)) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) + -1(x + -6)(x + -6) + -1(x + -4)(x + -4) = 0

Reorder the terms:
36 + 12x + x2 + -1(-6 + x)(x + -6) + -1(x + -4)(x + -4) = 0

Reorder the terms:
36 + 12x + x2 + -1(-6 + x)(-6 + x) + -1(x + -4)(x + -4) = 0

Multiply (-6 + x) * (-6 + x)
36 + 12x + x2 + -1(-6(-6 + x) + x(-6 + x)) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + -1((-6 * -6 + x * -6) + x(-6 + x)) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + -1((36 + -6x) + x(-6 + x)) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + -1(36 + -6x + (-6 * x + x * x)) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + -1(36 + -6x + (-6x + x2)) + -1(x + -4)(x + -4) = 0

Combine like terms: -6x + -6x = -12x
36 + 12x + x2 + -1(36 + -12x + x2) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + (36 * -1 + -12x * -1 + x2 * -1) + -1(x + -4)(x + -4) = 0
36 + 12x + x2 + (-36 + 12x + -1x2) + -1(x + -4)(x + -4) = 0

Reorder the terms:
36 + 12x + x2 + -36 + 12x + -1x2 + -1(-4 + x)(x + -4) = 0

Reorder the terms:
36 + 12x + x2 + -36 + 12x + -1x2 + -1(-4 + x)(-4 + x) = 0

Multiply (-4 + x) * (-4 + x)
36 + 12x + x2 + -36 + 12x + -1x2 + -1(-4(-4 + x) + x(-4 + x)) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + -1((-4 * -4 + x * -4) + x(-4 + x)) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + -1((16 + -4x) + x(-4 + x)) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + -1(16 + -4x + (-4 * x + x * x)) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + -1(16 + -4x + (-4x + x2)) = 0

Combine like terms: -4x + -4x = -8x
36 + 12x + x2 + -36 + 12x + -1x2 + -1(16 + -8x + x2) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + (16 * -1 + -8x * -1 + x2 * -1) = 0
36 + 12x + x2 + -36 + 12x + -1x2 + (-16 + 8x + -1x2) = 0

Reorder the terms:
36 + -36 + -16 + 12x + 12x + 8x + x2 + -1x2 + -1x2 = 0

Combine like terms: 36 + -36 = 0
0 + -16 + 12x + 12x + 8x + x2 + -1x2 + -1x2 = 0
-16 + 12x + 12x + 8x + x2 + -1x2 + -1x2 = 0

Combine like terms: 12x + 12x = 24x
-16 + 24x + 8x + x2 + -1x2 + -1x2 = 0

Combine like terms: 24x + 8x = 32x
-16 + 32x + x2 + -1x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
-16 + 32x + 0 + -1x2 = 0
-16 + 32x + -1x2 = 0

Solving
-16 + 32x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16 + -32x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -32x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -32x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -32x + x2 = 0 + -16
-32x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-32x + x2 = -16

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -16 + 256

Reorder the terms:
256 + -32x + x2 = -16 + 256

Combine like terms: -16 + 256 = 240
256 + -32x + x2 = 240

Factor a perfect square on the left side:
(x + -16)(x + -16) = 240

Calculate the square root of the right side: 15.491933385

Break this problem into two subproblems by setting 
(x + -16) equal to 15.491933385 and -15.491933385.


Subproblem 1
x + -16 = 15.491933385

Simplifying
x + -16 = 15.491933385

Reorder the terms:
-16 + x = 15.491933385

Solving
-16 + x = 15.491933385

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = 15.491933385 + 16

Combine like terms: -16 + 16 = 0
0 + x = 15.491933385 + 16
x = 15.491933385 + 16

Combine like terms: 15.491933385 + 16 = 31.491933385
x = 31.491933385

Simplifying
x = 31.491933385


Subproblem 2
x + -16 = -15.491933385

Simplifying
x + -16 = -15.491933385

Reorder the terms:
-16 + x = -15.491933385

Solving
-16 + x = -15.491933385

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = -15.491933385 + 16

Combine like terms: -16 + 16 = 0
0 + x = -15.491933385 + 16
x = -15.491933385 + 16

Combine like terms: -15.491933385 + 16 = 0.508066615
x = 0.508066615

Simplifying
x = 0.508066615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.491933385, 0.508066615}

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