96=(3x-6)(x-1)

Solution for 96=(3x-6)(x-1) equation:

Simplifying
96 = (3x + -6)(x + -1)

Reorder the terms:
96 = (-6 + 3x)(x + -1)

Reorder the terms:
96 = (-6 + 3x)(-1 + x)

Multiply (-6 + 3x) * (-1 + x)
96 = (-6(-1 + x) + 3x * (-1 + x))
96 = ((-1 * -6 + x * -6) + 3x * (-1 + x))
96 = ((6 + -6x) + 3x * (-1 + x))
96 = (6 + -6x + (-1 * 3x + x * 3x))
96 = (6 + -6x + (-3x + 3x2))

Combine like terms: -6x + -3x = -9x
96 = (6 + -9x + 3x2)

Solving
96 = 6 + -9x + 3x2

Solving for variable 'x'.

Combine like terms: 96 + -6 = 90
90 + 9x + -3x2 = 6 + -9x + 3x2 + -6 + 9x + -3x2

Reorder the terms:
90 + 9x + -3x2 = 6 + -6 + -9x + 9x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
90 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2
90 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
90 + 9x + -3x2 = 0 + 3x2 + -3x2
90 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
90 + 9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 3x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(30 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
30 + 3x + -1x2 = 0

Solving
30 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + -3x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -3x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -3x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -3x + x2 = 0 + 30
-3x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-3x + x2 = 30

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 = 30 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + -3x + x2 = 32.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + -1.5 = 5.678908346

Simplifying
x + -1.5 = 5.678908346

Reorder the terms:
-1.5 + x = 5.678908346

Solving
-1.5 + x = 5.678908346

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 = 5.678908346 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 5.678908346 + 1.5
x = 5.678908346 + 1.5

Combine like terms: 5.678908346 + 1.5 = 7.178908346
x = 7.178908346

Simplifying
x = 7.178908346

Subproblem 2
x + -1.5 = -5.678908346

Simplifying
x + -1.5 = -5.678908346

Reorder the terms:
-1.5 + x = -5.678908346

Solving
-1.5 + x = -5.678908346

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 = -5.678908346 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -5.678908346 + 1.5
x = -5.678908346 + 1.5

Combine like terms: -5.678908346 + 1.5 = -4.178908346
x = -4.178908346

Simplifying
x = -4.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.178908346, -4.178908346}
Solution
x = {7.178908346, -4.178908346}