8x-48+8x+48=(x+6)(x-6)8

Solution for 8x-48+8x+48=(x+6)(x-6)8 equation:

Simplifying
8x + -48 + 8x + 48 = (x + 6)(x + -6) * 8

Reorder the terms:
-48 + 48 + 8x + 8x = (x + 6)(x + -6) * 8

Combine like terms: -48 + 48 = 0
0 + 8x + 8x = (x + 6)(x + -6) * 8
8x + 8x = (x + 6)(x + -6) * 8

Combine like terms: 8x + 8x = 16x
16x = (x + 6)(x + -6) * 8

Reorder the terms:
16x = (6 + x)(x + -6) * 8

Reorder the terms:
16x = (6 + x)(-6 + x) * 8

Reorder the terms for easier multiplication:
16x = 8(6 + x)(-6 + x)

Multiply (6 + x) * (-6 + x)
16x = 8(6(-6 + x) + x(-6 + x))
16x = 8((-6 * 6 + x * 6) + x(-6 + x))
16x = 8((-36 + 6x) + x(-6 + x))
16x = 8(-36 + 6x + (-6 * x + x * x))
16x = 8(-36 + 6x + (-6x + x2))

Combine like terms: 6x + -6x = 0
16x = 8(-36 + 0 + x2)
16x = 8(-36 + x2)
16x = (-36 * 8 + x2 * 8)
16x = (-288 + 8x2)

Solving
16x = -288 + 8x2

Solving for variable 'x'.

Reorder the terms:
288 + 16x + -8x2 = -288 + 8x2 + 288 + -8x2

Reorder the terms:
288 + 16x + -8x2 = -288 + 288 + 8x2 + -8x2

Combine like terms: -288 + 288 = 0
288 + 16x + -8x2 = 0 + 8x2 + -8x2
288 + 16x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
288 + 16x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(36 + 2x + -1x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(36 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
36 + 2x + -1x2 = 0

Solving
36 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-36 + -2x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -2x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -2x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -2x + x2 = 0 + 36
-2x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-2x + x2 = 36

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 36 + 1

Reorder the terms:
1 + -2x + x2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + -2x + x2 = 37

Factor a perfect square on the left side:
(x + -1)(x + -1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -1) equal to 6.08276253 and -6.08276253.

Subproblem 1
x + -1 = 6.08276253

Simplifying
x + -1 = 6.08276253

Reorder the terms:
-1 + x = 6.08276253

Solving
-1 + x = 6.08276253

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.08276253 + 1
x = 6.08276253 + 1

Combine like terms: 6.08276253 + 1 = 7.08276253
x = 7.08276253

Simplifying
x = 7.08276253

Subproblem 2
x + -1 = -6.08276253

Simplifying
x + -1 = -6.08276253

Reorder the terms:
-1 + x = -6.08276253

Solving
-1 + x = -6.08276253

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.08276253 + 1
x = -6.08276253 + 1

Combine like terms: -6.08276253 + 1 = -5.08276253
x = -5.08276253

Simplifying
x = -5.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.08276253, -5.08276253}
Solution
x = {7.08276253, -5.08276253}