6x(4x+3)=92

Solution for 6x(4x+3)=92 equation:

Simplifying
6x(4x + 3) = 92

Reorder the terms:
6x(3 + 4x) = 92
(3 * 6x + 4x * 6x) = 92
(18x + 24x2) = 92

Solving
18x + 24x2 = 92

Solving for variable 'x'.

Reorder the terms:
-92 + 18x + 24x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + 18x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 9x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-46 + 9x + 12x2)' equal to zero and attempt to solve:

Simplifying
-46 + 9x + 12x2 = 0

Solving
-46 + 9x + 12x2 = 0

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

Divide each side by '12'.
-3.833333333 + 0.75x + x2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + 0.75x + 3.833333333 + x2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + 0.75x + x2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + 0.75x + x2 = 0 + 3.833333333
0.75x + x2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
0.75x + x2 = 3.833333333

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 3.833333333 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 3.833333333 + 0.140625

Combine like terms: 3.833333333 + 0.140625 = 3.973958333
0.140625 + 0.75x + x2 = 3.973958333

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 3.973958333

Calculate the square root of the right side: 1.993478952

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.993478952 and -1.993478952.

Subproblem 1
x + 0.375 = 1.993478952

Simplifying
x + 0.375 = 1.993478952

Reorder the terms:
0.375 + x = 1.993478952

Solving
0.375 + x = 1.993478952

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.993478952 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.993478952 + -0.375
x = 1.993478952 + -0.375

Combine like terms: 1.993478952 + -0.375 = 1.618478952
x = 1.618478952

Simplifying
x = 1.618478952

Subproblem 2
x + 0.375 = -1.993478952

Simplifying
x + 0.375 = -1.993478952

Reorder the terms:
0.375 + x = -1.993478952

Solving
0.375 + x = -1.993478952

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.993478952 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.993478952 + -0.375
x = -1.993478952 + -0.375

Combine like terms: -1.993478952 + -0.375 = -2.368478952
x = -2.368478952

Simplifying
x = -2.368478952

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.618478952, -2.368478952}
Solution
x = {1.618478952, -2.368478952}