(16x-4)(9x-6)=58

Solution for (16x-4)(9x-6)=58 equation:

Simplifying
(16x + -4)(9x + -6) = 58

Reorder the terms:
(-4 + 16x)(9x + -6) = 58

Reorder the terms:
(-4 + 16x)(-6 + 9x) = 58

Multiply (-4 + 16x) * (-6 + 9x)
(-4(-6 + 9x) + 16x * (-6 + 9x)) = 58
((-6 * -4 + 9x * -4) + 16x * (-6 + 9x)) = 58
((24 + -36x) + 16x * (-6 + 9x)) = 58
(24 + -36x + (-6 * 16x + 9x * 16x)) = 58
(24 + -36x + (-96x + 144x2)) = 58

Combine like terms: -36x + -96x = -132x
(24 + -132x + 144x2) = 58

Solving
24 + -132x + 144x2 = 58

Solving for variable 'x'.

Reorder the terms:
24 + -58 + -132x + 144x2 = 58 + -58

Combine like terms: 24 + -58 = -34
-34 + -132x + 144x2 = 58 + -58

Combine like terms: 58 + -58 = 0
-34 + -132x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -66x + 72x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -66x + 72x2)' equal to zero and attempt to solve:

Simplifying
-17 + -66x + 72x2 = 0

Solving
-17 + -66x + 72x2 = 0

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

Divide each side by '72'.
-0.2361111111 + -0.9166666667x + x2 = 0

Move the constant term to the right:

Add '0.2361111111' to each side of the equation.
-0.2361111111 + -0.9166666667x + 0.2361111111 + x2 = 0 + 0.2361111111

Reorder the terms:
-0.2361111111 + 0.2361111111 + -0.9166666667x + x2 = 0 + 0.2361111111

Combine like terms: -0.2361111111 + 0.2361111111 = 0.0000000000
0.0000000000 + -0.9166666667x + x2 = 0 + 0.2361111111
-0.9166666667x + x2 = 0 + 0.2361111111

Combine like terms: 0 + 0.2361111111 = 0.2361111111
-0.9166666667x + x2 = 0.2361111111

The x term is -0.9166666667x.  Take half its coefficient (-0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
-0.9166666667x + 0.2100694445 + x2 = 0.2361111111 + 0.2100694445

Reorder the terms:
0.2100694445 + -0.9166666667x + x2 = 0.2361111111 + 0.2100694445

Combine like terms: 0.2361111111 + 0.2100694445 = 0.4461805556
0.2100694445 + -0.9166666667x + x2 = 0.4461805556

Factor a perfect square on the left side:
(x + -0.4583333334)(x + -0.4583333334) = 0.4461805556

Calculate the square root of the right side: 0.667967481

Break this problem into two subproblems by setting 
(x + -0.4583333334) equal to 0.667967481 and -0.667967481.

Subproblem 1
x + -0.4583333334 = 0.667967481

Simplifying
x + -0.4583333334 = 0.667967481

Reorder the terms:
-0.4583333334 + x = 0.667967481

Solving
-0.4583333334 + x = 0.667967481

Solving for variable 'x'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + x = 0.667967481 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + x = 0.667967481 + 0.4583333334
x = 0.667967481 + 0.4583333334

Combine like terms: 0.667967481 + 0.4583333334 = 1.1263008144
x = 1.1263008144

Simplifying
x = 1.1263008144

Subproblem 2
x + -0.4583333334 = -0.667967481

Simplifying
x + -0.4583333334 = -0.667967481

Reorder the terms:
-0.4583333334 + x = -0.667967481

Solving
-0.4583333334 + x = -0.667967481

Solving for variable 'x'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + x = -0.667967481 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + x = -0.667967481 + 0.4583333334
x = -0.667967481 + 0.4583333334

Combine like terms: -0.667967481 + 0.4583333334 = -0.2096341476
x = -0.2096341476

Simplifying
x = -0.2096341476

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1263008144, -0.2096341476}
Solution
x = {1.1263008144, -0.2096341476}