8x(6x+4)=6

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


Simplifying
8x(6x + 4) = 6

Reorder the terms:
8x(4 + 6x) = 6
(4 * 8x + 6x * 8x) = 6
(32x + 48x2) = 6

Solving
32x + 48x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 32x + 48x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 32x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 16x + 24x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + 16x + 24x2)' equal to zero and attempt to solve:

Simplifying
-3 + 16x + 24x2 = 0

Solving
-3 + 16x + 24x2 = 0

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

Divide each side by '24'.
-0.125 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.6666666667x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.6666666667x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.6666666667x + x2 = 0 + 0.125
0.6666666667x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.6666666667x + x2 = 0.125

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 = 0.125 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.125 + 0.1111111112

Combine like terms: 0.125 + 0.1111111112 = 0.2361111112
0.1111111112 + 0.6666666667x + x2 = 0.2361111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.2361111112

Calculate the square root of the right side: 0.485912658

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.485912658 and -0.485912658.


Subproblem 1
x + 0.3333333334 = 0.485912658

Simplifying
x + 0.3333333334 = 0.485912658

Reorder the terms:
0.3333333334 + x = 0.485912658

Solving
0.3333333334 + x = 0.485912658

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 = 0.485912658 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.485912658 + -0.3333333334
x = 0.485912658 + -0.3333333334

Combine like terms: 0.485912658 + -0.3333333334 = 0.1525793246
x = 0.1525793246

Simplifying
x = 0.1525793246


Subproblem 2
x + 0.3333333334 = -0.485912658

Simplifying
x + 0.3333333334 = -0.485912658

Reorder the terms:
0.3333333334 + x = -0.485912658

Solving
0.3333333334 + x = -0.485912658

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 = -0.485912658 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.485912658 + -0.3333333334
x = -0.485912658 + -0.3333333334

Combine like terms: -0.485912658 + -0.3333333334 = -0.8192459914
x = -0.8192459914

Simplifying
x = -0.8192459914


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1525793246, -0.8192459914}
Solution
x = {0.1525793246, -0.8192459914}

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