(4x-2)(3x-1)=92

Solution for (4x-2)(3x-1)=92 equation:

Simplifying
(4x + -2)(3x + -1) = 92

Reorder the terms:
(-2 + 4x)(3x + -1) = 92

Reorder the terms:
(-2 + 4x)(-1 + 3x) = 92

Multiply (-2 + 4x) * (-1 + 3x)
(-2(-1 + 3x) + 4x * (-1 + 3x)) = 92
((-1 * -2 + 3x * -2) + 4x * (-1 + 3x)) = 92
((2 + -6x) + 4x * (-1 + 3x)) = 92
(2 + -6x + (-1 * 4x + 3x * 4x)) = 92
(2 + -6x + (-4x + 12x2)) = 92

Combine like terms: -6x + -4x = -10x
(2 + -10x + 12x2) = 92

Solving
2 + -10x + 12x2 = 92

Solving for variable 'x'.

Reorder the terms:
2 + -92 + -10x + 12x2 = 92 + -92

Combine like terms: 2 + -92 = -90
-90 + -10x + 12x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-90 + -10x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -5x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + -5x + 6x2)' equal to zero and attempt to solve:

Simplifying
-45 + -5x + 6x2 = 0

Solving
-45 + -5x + 6x2 = 0

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

Divide each side by '6'.
-7.5 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -0.8333333333x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -0.8333333333x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -0.8333333333x + x2 = 0 + 7.5
-0.8333333333x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-0.8333333333x + x2 = 7.5

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 7.5 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 7.5 + 0.1736111111

Combine like terms: 7.5 + 0.1736111111 = 7.6736111111
0.1736111111 + -0.8333333333x + x2 = 7.6736111111

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 7.6736111111

Calculate the square root of the right side: 2.770128356

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 2.770128356 and -2.770128356.

Subproblem 1
x + -0.4166666667 = 2.770128356

Simplifying
x + -0.4166666667 = 2.770128356

Reorder the terms:
-0.4166666667 + x = 2.770128356

Solving
-0.4166666667 + x = 2.770128356

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 2.770128356 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 2.770128356 + 0.4166666667
x = 2.770128356 + 0.4166666667

Combine like terms: 2.770128356 + 0.4166666667 = 3.1867950227
x = 3.1867950227

Simplifying
x = 3.1867950227

Subproblem 2
x + -0.4166666667 = -2.770128356

Simplifying
x + -0.4166666667 = -2.770128356

Reorder the terms:
-0.4166666667 + x = -2.770128356

Solving
-0.4166666667 + x = -2.770128356

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -2.770128356 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -2.770128356 + 0.4166666667
x = -2.770128356 + 0.4166666667

Combine like terms: -2.770128356 + 0.4166666667 = -2.3534616893
x = -2.3534616893

Simplifying
x = -2.3534616893

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.1867950227, -2.3534616893}
Solution
x = {3.1867950227, -2.3534616893}