6=2(x+8)5x

Solution for 6=2(x+8)5x equation:

Simplifying
6 = 2(x + 8) * 5x

Reorder the terms:
6 = 2(8 + x) * 5x

Reorder the terms for easier multiplication:
6 = 2 * 5x(8 + x)

Multiply 2 * 5
6 = 10x(8 + x)
6 = (8 * 10x + x * 10x)
6 = (80x + 10x2)

Solving
6 = 80x + 10x2

Solving for variable 'x'.

Reorder the terms:
6 + -80x + -10x2 = 80x + -80x + 10x2 + -10x2

Combine like terms: 80x + -80x = 0
6 + -80x + -10x2 = 0 + 10x2 + -10x2
6 + -80x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
6 + -80x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -40x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -40x + -5x2)' equal to zero and attempt to solve:

Simplifying
3 + -40x + -5x2 = 0

Solving
3 + -40x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + 8x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 8x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 8x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 8x + x2 = 0 + 0.6
8x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
8x + x2 = 0.6

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 = 0.6 + 16

Reorder the terms:
16 + 8x + x2 = 0.6 + 16

Combine like terms: 0.6 + 16 = 16.6
16 + 8x + x2 = 16.6

Factor a perfect square on the left side:
(x + 4)(x + 4) = 16.6

Calculate the square root of the right side: 4.074309757

Break this problem into two subproblems by setting 
(x + 4) equal to 4.074309757 and -4.074309757.

Subproblem 1
x + 4 = 4.074309757

Simplifying
x + 4 = 4.074309757

Reorder the terms:
4 + x = 4.074309757

Solving
4 + x = 4.074309757

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 = 4.074309757 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.074309757 + -4
x = 4.074309757 + -4

Combine like terms: 4.074309757 + -4 = 0.074309757
x = 0.074309757

Simplifying
x = 0.074309757

Subproblem 2
x + 4 = -4.074309757

Simplifying
x + 4 = -4.074309757

Reorder the terms:
4 + x = -4.074309757

Solving
4 + x = -4.074309757

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 = -4.074309757 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.074309757 + -4
x = -4.074309757 + -4

Combine like terms: -4.074309757 + -4 = -8.074309757
x = -8.074309757

Simplifying
x = -8.074309757

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.074309757, -8.074309757}
Solution
x = {0.074309757, -8.074309757}