(3x-9)(-8x)=6

Solution for (3x-9)(-8x)=6 equation:

Simplifying
(3x + -9)(-8x) = 6

Reorder the terms:
(-9 + 3x)(-8x) = 6

Remove parenthesis around (-8x)
(-9 + 3x) * -8x = 6

Reorder the terms for easier multiplication:
-8x(-9 + 3x) = 6
(-9 * -8x + 3x * -8x) = 6
(72x + -24x2) = 6

Solving
72x + -24x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 72x + -24x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 72x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 12x + -4x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + 12x + -4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + -4x2 = 0

Solving
-1 + 12x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -3x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -3x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -3x + x2 = 0 + -0.25
-3x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-3x + x2 = -0.25

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.25 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.25 + 2.25

Combine like terms: -0.25 + 2.25 = 2
2.25 + -3x + x2 = 2

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -1.5 = 1.414213562

Simplifying
x + -1.5 = 1.414213562

Reorder the terms:
-1.5 + x = 1.414213562

Solving
-1.5 + x = 1.414213562

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.414213562 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.414213562 + 1.5
x = 1.414213562 + 1.5

Combine like terms: 1.414213562 + 1.5 = 2.914213562
x = 2.914213562

Simplifying
x = 2.914213562

Subproblem 2
x + -1.5 = -1.414213562

Simplifying
x + -1.5 = -1.414213562

Reorder the terms:
-1.5 + x = -1.414213562

Solving
-1.5 + x = -1.414213562

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.414213562 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.414213562 + 1.5
x = -1.414213562 + 1.5

Combine like terms: -1.414213562 + 1.5 = 0.085786438
x = 0.085786438

Simplifying
x = 0.085786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.914213562, 0.085786438}
Solution
x = {2.914213562, 0.085786438}