3x=(x+8)(x-4)

Solution for 3x=(x+8)(x-4) equation:

Simplifying
3x = (x + 8)(x + -4)

Reorder the terms:
3x = (8 + x)(x + -4)

Reorder the terms:
3x = (8 + x)(-4 + x)

Multiply (8 + x) * (-4 + x)
3x = (8(-4 + x) + x(-4 + x))
3x = ((-4 * 8 + x * 8) + x(-4 + x))
3x = ((-32 + 8x) + x(-4 + x))
3x = (-32 + 8x + (-4 * x + x * x))
3x = (-32 + 8x + (-4x + x2))

Combine like terms: 8x + -4x = 4x
3x = (-32 + 4x + x2)

Solving
3x = -32 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
32 + 3x + -4x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2

Combine like terms: 3x + -4x = -1x
32 + -1x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2

Reorder the terms:
32 + -1x + -1x2 = -32 + 32 + 4x + -4x + x2 + -1x2

Combine like terms: -32 + 32 = 0
32 + -1x + -1x2 = 0 + 4x + -4x + x2 + -1x2
32 + -1x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
32 + -1x + -1x2 = 0 + x2 + -1x2
32 + -1x + -1x2 = x2 + -1x2

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

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

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

Move the constant term to the right:

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

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

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

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

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.
 + 0.25 + x2 = 32 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
1.25 + x2 = 32.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 0.5 = 5.678908346

Simplifying
x + 0.5 = 5.678908346

Reorder the terms:
0.5 + x = 5.678908346

Solving
0.5 + x = 5.678908346

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 = 5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.678908346 + -0.5
x = 5.678908346 + -0.5

Combine like terms: 5.678908346 + -0.5 = 5.178908346
x = 5.178908346

Simplifying
x = 5.178908346

Subproblem 2
x + 0.5 = -5.678908346

Simplifying
x + 0.5 = -5.678908346

Reorder the terms:
0.5 + x = -5.678908346

Solving
0.5 + x = -5.678908346

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 = -5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.678908346 + -0.5
x = -5.678908346 + -0.5

Combine like terms: -5.678908346 + -0.5 = -6.178908346
x = -6.178908346

Simplifying
x = -6.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.178908346, -6.178908346}