6(5+3x)4x=34

Solution for 6(5+3x)4x=34 equation:

Simplifying
6(5 + 3x) * 4x = 34

Reorder the terms for easier multiplication:
6 * 4x(5 + 3x) = 34

Multiply 6 * 4
24x(5 + 3x) = 34
(5 * 24x + 3x * 24x) = 34
(120x + 72x2) = 34

Solving
120x + 72x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 120x + 72x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 120x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 60x + 36x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 60x + 36x2)' equal to zero and attempt to solve:

Simplifying
-17 + 60x + 36x2 = 0

Solving
-17 + 60x + 36x2 = 0

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

Divide each side by '36'.
-0.4722222222 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.4722222222' to each side of the equation.
-0.4722222222 + 1.666666667x + 0.4722222222 + x2 = 0 + 0.4722222222

Reorder the terms:
-0.4722222222 + 0.4722222222 + 1.666666667x + x2 = 0 + 0.4722222222

Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + 0.4722222222
1.666666667x + x2 = 0 + 0.4722222222

Combine like terms: 0 + 0.4722222222 = 0.4722222222
1.666666667x + x2 = 0.4722222222

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.4722222222 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.4722222222 + 0.6944444447

Combine like terms: 0.4722222222 + 0.6944444447 = 1.1666666669
0.6944444447 + 1.666666667x + x2 = 1.1666666669

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.1666666669

Calculate the square root of the right side: 1.08012345

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.08012345 and -1.08012345.

Subproblem 1
x + 0.8333333335 = 1.08012345

Simplifying
x + 0.8333333335 = 1.08012345

Reorder the terms:
0.8333333335 + x = 1.08012345

Solving
0.8333333335 + x = 1.08012345

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.08012345 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.08012345 + -0.8333333335
x = 1.08012345 + -0.8333333335

Combine like terms: 1.08012345 + -0.8333333335 = 0.2467901165
x = 0.2467901165

Simplifying
x = 0.2467901165

Subproblem 2
x + 0.8333333335 = -1.08012345

Simplifying
x + 0.8333333335 = -1.08012345

Reorder the terms:
0.8333333335 + x = -1.08012345

Solving
0.8333333335 + x = -1.08012345

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.08012345 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.08012345 + -0.8333333335
x = -1.08012345 + -0.8333333335

Combine like terms: -1.08012345 + -0.8333333335 = -1.9134567835
x = -1.9134567835

Simplifying
x = -1.9134567835

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2467901165, -1.9134567835}
Solution
x = {0.2467901165, -1.9134567835}