-8-5(1+6x)=5(1-6x)2x

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Solution for -8-5(1+6x)=5(1-6x)2x equation: 


Simplifying
-8 + -5(1 + 6x) = 5(1 + -6x) * 2x
-8 + (1 * -5 + 6x * -5) = 5(1 + -6x) * 2x
-8 + (-5 + -30x) = 5(1 + -6x) * 2x

Combine like terms: -8 + -5 = -13
-13 + -30x = 5(1 + -6x) * 2x

Reorder the terms for easier multiplication:
-13 + -30x = 5 * 2x(1 + -6x)

Multiply 5 * 2
-13 + -30x = 10x(1 + -6x)
-13 + -30x = (1 * 10x + -6x * 10x)
-13 + -30x = (10x + -60x2)

Solving
-13 + -30x = 10x + -60x2

Solving for variable 'x'.

Combine like terms: -30x + -10x = -40x
-13 + -40x + 60x2 = 10x + -60x2 + -10x + 60x2

Reorder the terms:
-13 + -40x + 60x2 = 10x + -10x + -60x2 + 60x2

Combine like terms: 10x + -10x = 0
-13 + -40x + 60x2 = 0 + -60x2 + 60x2
-13 + -40x + 60x2 = -60x2 + 60x2

Combine like terms: -60x2 + 60x2 = 0
-13 + -40x + 60x2 = 0

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

Divide each side by '60'.
-0.2166666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.2166666667' to each side of the equation.
-0.2166666667 + -0.6666666667x + 0.2166666667 + x2 = 0 + 0.2166666667

Reorder the terms:
-0.2166666667 + 0.2166666667 + -0.6666666667x + x2 = 0 + 0.2166666667

Combine like terms: -0.2166666667 + 0.2166666667 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + 0.2166666667
-0.6666666667x + x2 = 0 + 0.2166666667

Combine like terms: 0 + 0.2166666667 = 0.2166666667
-0.6666666667x + x2 = 0.2166666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 0.2166666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.2166666667 + 0.1111111112

Combine like terms: 0.2166666667 + 0.1111111112 = 0.3277777779
0.1111111112 + -0.6666666667x + x2 = 0.3277777779

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.3277777779

Calculate the square root of the right side: 0.572518801

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.572518801 and -0.572518801.


Subproblem 1
x + -0.3333333334 = 0.572518801

Simplifying
x + -0.3333333334 = 0.572518801

Reorder the terms:
-0.3333333334 + x = 0.572518801

Solving
-0.3333333334 + x = 0.572518801

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 0.572518801 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 0.572518801 + 0.3333333334
x = 0.572518801 + 0.3333333334

Combine like terms: 0.572518801 + 0.3333333334 = 0.9058521344
x = 0.9058521344

Simplifying
x = 0.9058521344


Subproblem 2
x + -0.3333333334 = -0.572518801

Simplifying
x + -0.3333333334 = -0.572518801

Reorder the terms:
-0.3333333334 + x = -0.572518801

Solving
-0.3333333334 + x = -0.572518801

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -0.572518801 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -0.572518801 + 0.3333333334
x = -0.572518801 + 0.3333333334

Combine like terms: -0.572518801 + 0.3333333334 = -0.2391854676
x = -0.2391854676

Simplifying
x = -0.2391854676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9058521344, -0.2391854676}

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