6(x+8)x=7

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Solution for 6(x+8)x=7 equation: 


Simplifying
6(x + 8) * x = 7

Reorder the terms:
6(8 + x) * x = 7

Reorder the terms for easier multiplication:
6x(8 + x) = 7
(8 * 6x + x * 6x) = 7
(48x + 6x2) = 7

Solving
48x + 6x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 48x + 6x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 48x + 6x2 = 0

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

Divide each side by '6'.
-1.166666667 + 8x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 8x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 8x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 8x + x2 = 0 + 1.166666667
8x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
8x + x2 = 1.166666667

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 = 1.166666667 + 16

Reorder the terms:
16 + 8x + x2 = 1.166666667 + 16

Combine like terms: 1.166666667 + 16 = 17.166666667
16 + 8x + x2 = 17.166666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 17.166666667

Calculate the square root of the right side: 4.143267632

Break this problem into two subproblems by setting 
(x + 4) equal to 4.143267632 and -4.143267632.


Subproblem 1
x + 4 = 4.143267632

Simplifying
x + 4 = 4.143267632

Reorder the terms:
4 + x = 4.143267632

Solving
4 + x = 4.143267632

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 = 4.143267632 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.143267632 + -4
x = 4.143267632 + -4

Combine like terms: 4.143267632 + -4 = 0.143267632
x = 0.143267632

Simplifying
x = 0.143267632


Subproblem 2
x + 4 = -4.143267632

Simplifying
x + 4 = -4.143267632

Reorder the terms:
4 + x = -4.143267632

Solving
4 + x = -4.143267632

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 = -4.143267632 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.143267632 + -4
x = -4.143267632 + -4

Combine like terms: -4.143267632 + -4 = -8.143267632
x = -8.143267632

Simplifying
x = -8.143267632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.143267632, -8.143267632}

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