-5-(x+8)6x=4(x+2)

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Solution for -5-(x+8)6x=4(x+2) equation: 


Simplifying
-5 + -1(x + 8) * 6x = 4(x + 2)

Reorder the terms:
-5 + -1(8 + x) * 6x = 4(x + 2)

Reorder the terms for easier multiplication:
-5 + -1 * 6x(8 + x) = 4(x + 2)

Multiply -1 * 6
-5 + -6x(8 + x) = 4(x + 2)
-5 + (8 * -6x + x * -6x) = 4(x + 2)
-5 + (-48x + -6x2) = 4(x + 2)

Reorder the terms:
-5 + -48x + -6x2 = 4(2 + x)
-5 + -48x + -6x2 = (2 * 4 + x * 4)
-5 + -48x + -6x2 = (8 + 4x)

Solving
-5 + -48x + -6x2 = 8 + 4x

Solving for variable 'x'.

Reorder the terms:
-5 + -8 + -48x + -4x + -6x2 = 8 + 4x + -8 + -4x

Combine like terms: -5 + -8 = -13
-13 + -48x + -4x + -6x2 = 8 + 4x + -8 + -4x

Combine like terms: -48x + -4x = -52x
-13 + -52x + -6x2 = 8 + 4x + -8 + -4x

Reorder the terms:
-13 + -52x + -6x2 = 8 + -8 + 4x + -4x

Combine like terms: 8 + -8 = 0
-13 + -52x + -6x2 = 0 + 4x + -4x
-13 + -52x + -6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-13 + -52x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 52x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(13 + 52x + 6x2)' equal to zero and attempt to solve:

Simplifying
13 + 52x + 6x2 = 0

Solving
13 + 52x + 6x2 = 0

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

Divide each side by '6'.
2.166666667 + 8.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.166666667' to each side of the equation.
2.166666667 + 8.666666667x + -2.166666667 + x2 = 0 + -2.166666667

Reorder the terms:
2.166666667 + -2.166666667 + 8.666666667x + x2 = 0 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + 8.666666667x + x2 = 0 + -2.166666667
8.666666667x + x2 = 0 + -2.166666667

Combine like terms: 0 + -2.166666667 = -2.166666667
8.666666667x + x2 = -2.166666667

The x term is 8.666666667x.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667x + 18.77777778 + x2 = -2.166666667 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667x + x2 = -2.166666667 + 18.77777778

Combine like terms: -2.166666667 + 18.77777778 = 16.611111113
18.77777778 + 8.666666667x + x2 = 16.611111113

Factor a perfect square on the left side:
(x + 4.333333334)(x + 4.333333334) = 16.611111113

Calculate the square root of the right side: 4.075673087

Break this problem into two subproblems by setting 
(x + 4.333333334) equal to 4.075673087 and -4.075673087.


Subproblem 1
x + 4.333333334 = 4.075673087

Simplifying
x + 4.333333334 = 4.075673087

Reorder the terms:
4.333333334 + x = 4.075673087

Solving
4.333333334 + x = 4.075673087

Solving for variable 'x'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + x = 4.075673087 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = 4.075673087 + -4.333333334
x = 4.075673087 + -4.333333334

Combine like terms: 4.075673087 + -4.333333334 = -0.257660247
x = -0.257660247

Simplifying
x = -0.257660247


Subproblem 2
x + 4.333333334 = -4.075673087

Simplifying
x + 4.333333334 = -4.075673087

Reorder the terms:
4.333333334 + x = -4.075673087

Solving
4.333333334 + x = -4.075673087

Solving for variable 'x'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + x = -4.075673087 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = -4.075673087 + -4.333333334
x = -4.075673087 + -4.333333334

Combine like terms: -4.075673087 + -4.333333334 = -8.409006421
x = -8.409006421

Simplifying
x = -8.409006421


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.257660247, -8.409006421}
Solution
x = {-0.257660247, -8.409006421}

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