8x(2x+8)=4

Solution for 8x(2x+8)=4 equation:

Simplifying
8x(2x + 8) = 4

Reorder the terms:
8x(8 + 2x) = 4
(8 * 8x + 2x * 8x) = 4
(64x + 16x2) = 4

Solving
64x + 16x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 64x + 16x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 64x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 16x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 16x + 4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 16x + 4x2 = 0

Solving
-1 + 16x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 4x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 4x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 4x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 4x + x2 = 0 + 0.25
4x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
4x + x2 = 0.25

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 0.25 + 4

Reorder the terms:
4 + 4x + x2 = 0.25 + 4

Combine like terms: 0.25 + 4 = 4.25
4 + 4x + x2 = 4.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 2) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + 2 = 2.061552813

Simplifying
x + 2 = 2.061552813

Reorder the terms:
2 + x = 2.061552813

Solving
2 + x = 2.061552813

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.061552813 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.061552813 + -2
x = 2.061552813 + -2

Combine like terms: 2.061552813 + -2 = 0.061552813
x = 0.061552813

Simplifying
x = 0.061552813

Subproblem 2
x + 2 = -2.061552813

Simplifying
x + 2 = -2.061552813

Reorder the terms:
2 + x = -2.061552813

Solving
2 + x = -2.061552813

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.061552813 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.061552813 + -2
x = -2.061552813 + -2

Combine like terms: -2.061552813 + -2 = -4.061552813
x = -4.061552813

Simplifying
x = -4.061552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.061552813, -4.061552813}
Solution
x = {0.061552813, -4.061552813}