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

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

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

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

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

Multiply (4 + x) * (4 + x)
3(4(4 + x) + x(4 + x)) = 8
3((4 * 4 + x * 4) + x(4 + x)) = 8
3((16 + 4x) + x(4 + x)) = 8
3(16 + 4x + (4 * x + x * x)) = 8
3(16 + 4x + (4x + x2)) = 8

Combine like terms: 4x + 4x = 8x
3(16 + 8x + x2) = 8
(16 * 3 + 8x * 3 + x2 * 3) = 8
(48 + 24x + 3x2) = 8

Solving
48 + 24x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
48 + -8 + 24x + 3x2 = 8 + -8

Combine like terms: 48 + -8 = 40
40 + 24x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
40 + 24x + 3x2 = 0

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

Divide each side by '3'.
13.33333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + 8x + -13.33333333 + x2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + 8x + x2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + 8x + x2 = 0 + -13.33333333
8x + x2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
8x + x2 = -13.33333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -13.33333333 + 16

Reorder the terms:
16 + 8x + x2 = -13.33333333 + 16

Combine like terms: -13.33333333 + 16 = 2.66666667
16 + 8x + x2 = 2.66666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 2.66666667

Calculate the square root of the right side: 1.632993163

Break this problem into two subproblems by setting 
(x + 4) equal to 1.632993163 and -1.632993163.

Subproblem 1
x + 4 = 1.632993163

Simplifying
x + 4 = 1.632993163

Reorder the terms:
4 + x = 1.632993163

Solving
4 + x = 1.632993163

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 1.632993163 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.632993163 + -4
x = 1.632993163 + -4

Combine like terms: 1.632993163 + -4 = -2.367006837
x = -2.367006837

Simplifying
x = -2.367006837

Subproblem 2
x + 4 = -1.632993163

Simplifying
x + 4 = -1.632993163

Reorder the terms:
4 + x = -1.632993163

Solving
4 + x = -1.632993163

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -1.632993163 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.632993163 + -4
x = -1.632993163 + -4

Combine like terms: -1.632993163 + -4 = -5.632993163
x = -5.632993163

Simplifying
x = -5.632993163

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.367006837, -5.632993163}