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

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

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

Reorder the terms:
8(6 + x) = 4(x + -6) * 4x
(6 * 8 + x * 8) = 4(x + -6) * 4x
(48 + 8x) = 4(x + -6) * 4x

Reorder the terms:
48 + 8x = 4(-6 + x) * 4x

Reorder the terms for easier multiplication:
48 + 8x = 4 * 4x(-6 + x)

Multiply 4 * 4
48 + 8x = 16x(-6 + x)
48 + 8x = (-6 * 16x + x * 16x)
48 + 8x = (-96x + 16x2)

Solving
48 + 8x = -96x + 16x2

Solving for variable 'x'.

Combine like terms: 8x + 96x = 104x
48 + 104x + -16x2 = -96x + 16x2 + 96x + -16x2

Reorder the terms:
48 + 104x + -16x2 = -96x + 96x + 16x2 + -16x2

Combine like terms: -96x + 96x = 0
48 + 104x + -16x2 = 0 + 16x2 + -16x2
48 + 104x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
48 + 104x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + 13x + -2x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(6 + 13x + -2x2)' equal to zero and attempt to solve:

Simplifying
6 + 13x + -2x2 = 0

Solving
6 + 13x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + -6.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -6.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6.5x + x2 = 0 + 3
-6.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6.5x + x2 = 3

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 3 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 3 + 10.5625

Combine like terms: 3 + 10.5625 = 13.5625
10.5625 + -6.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.682729966 and -3.682729966.

Subproblem 1
x + -3.25 = 3.682729966

Simplifying
x + -3.25 = 3.682729966

Reorder the terms:
-3.25 + x = 3.682729966

Solving
-3.25 + x = 3.682729966

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.682729966 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.682729966 + 3.25
x = 3.682729966 + 3.25

Combine like terms: 3.682729966 + 3.25 = 6.932729966
x = 6.932729966

Simplifying
x = 6.932729966

Subproblem 2
x + -3.25 = -3.682729966

Simplifying
x + -3.25 = -3.682729966

Reorder the terms:
-3.25 + x = -3.682729966

Solving
-3.25 + x = -3.682729966

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.682729966 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.682729966 + 3.25
x = -3.682729966 + 3.25

Combine like terms: -3.682729966 + 3.25 = -0.432729966
x = -0.432729966

Simplifying
x = -0.432729966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.932729966, -0.432729966}
Solution
x = {6.932729966, -0.432729966}