0.5(5+7)=8x(4x+6)

Solution for 0.5(5+7)=8x(4x+6) equation:

Simplifying
0.5(5 + 7) = 8x(4x + 6)

Combine like terms: 5 + 7 = 12
0.5(12) = 8x(4x + 6)

Multiply 0.5 * 12
6 = 8x(4x + 6)

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

Solving
6 = 48x + 32x2

Solving for variable 'x'.

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

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

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -24x + -16x2)' equal to zero and attempt to solve:

Simplifying
3 + -24x + -16x2 = 0

Solving
3 + -24x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.1875 + 1.5x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + 1.5x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + 1.5x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + 1.5x + x2 = 0 + 0.1875
1.5x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
1.5x + x2 = 0.1875

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 0.1875 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.1875 + 0.5625

Combine like terms: 0.1875 + 0.5625 = 0.75
0.5625 + 1.5x + x2 = 0.75

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.866025404 and -0.866025404.

Subproblem 1
x + 0.75 = 0.866025404

Simplifying
x + 0.75 = 0.866025404

Reorder the terms:
0.75 + x = 0.866025404

Solving
0.75 + x = 0.866025404

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 0.866025404 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.866025404 + -0.75
x = 0.866025404 + -0.75

Combine like terms: 0.866025404 + -0.75 = 0.116025404
x = 0.116025404

Simplifying
x = 0.116025404

Subproblem 2
x + 0.75 = -0.866025404

Simplifying
x + 0.75 = -0.866025404

Reorder the terms:
0.75 + x = -0.866025404

Solving
0.75 + x = -0.866025404

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -0.866025404 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.866025404 + -0.75
x = -0.866025404 + -0.75

Combine like terms: -0.866025404 + -0.75 = -1.616025404
x = -1.616025404

Simplifying
x = -1.616025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.116025404, -1.616025404}
Solution
x = {0.116025404, -1.616025404}