(3x-1)(x-9)=(x+2)(x-4)

Solution for (3x-1)(x-9)=(x+2)(x-4) equation:

Simplifying
(3x + -1)(x + -9) = (x + 2)(x + -4)

Reorder the terms:
(-1 + 3x)(x + -9) = (x + 2)(x + -4)

Reorder the terms:
(-1 + 3x)(-9 + x) = (x + 2)(x + -4)

Multiply (-1 + 3x) * (-9 + x)
(-1(-9 + x) + 3x * (-9 + x)) = (x + 2)(x + -4)
((-9 * -1 + x * -1) + 3x * (-9 + x)) = (x + 2)(x + -4)
((9 + -1x) + 3x * (-9 + x)) = (x + 2)(x + -4)
(9 + -1x + (-9 * 3x + x * 3x)) = (x + 2)(x + -4)
(9 + -1x + (-27x + 3x2)) = (x + 2)(x + -4)

Combine like terms: -1x + -27x = -28x
(9 + -28x + 3x2) = (x + 2)(x + -4)

Reorder the terms:
9 + -28x + 3x2 = (2 + x)(x + -4)

Reorder the terms:
9 + -28x + 3x2 = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
9 + -28x + 3x2 = (2(-4 + x) + x(-4 + x))
9 + -28x + 3x2 = ((-4 * 2 + x * 2) + x(-4 + x))
9 + -28x + 3x2 = ((-8 + 2x) + x(-4 + x))
9 + -28x + 3x2 = (-8 + 2x + (-4 * x + x * x))
9 + -28x + 3x2 = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
9 + -28x + 3x2 = (-8 + -2x + x2)

Solving
9 + -28x + 3x2 = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
9 + 8 + -28x + 2x + 3x2 + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 9 + 8 = 17
17 + -28x + 2x + 3x2 + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -28x + 2x = -26x
17 + -26x + 3x2 + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
17 + -26x + 2x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
17 + -26x + 2x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
17 + -26x + 2x2 = 0 + -2x + 2x + x2 + -1x2
17 + -26x + 2x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
17 + -26x + 2x2 = 0 + x2 + -1x2
17 + -26x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
17 + -26x + 2x2 = 0

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

Divide each side by '2'.
8.5 + -13x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -13x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -13x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -13x + x2 = 0 + -8.5
-13x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-13x + x2 = -8.5

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -8.5 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -8.5 + 42.25

Combine like terms: -8.5 + 42.25 = 33.75
42.25 + -13x + x2 = 33.75

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 33.75

Calculate the square root of the right side: 5.809475019

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.809475019 and -5.809475019.

Subproblem 1
x + -6.5 = 5.809475019

Simplifying
x + -6.5 = 5.809475019

Reorder the terms:
-6.5 + x = 5.809475019

Solving
-6.5 + x = 5.809475019

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 5.809475019 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 5.809475019 + 6.5
x = 5.809475019 + 6.5

Combine like terms: 5.809475019 + 6.5 = 12.309475019
x = 12.309475019

Simplifying
x = 12.309475019

Subproblem 2
x + -6.5 = -5.809475019

Simplifying
x + -6.5 = -5.809475019

Reorder the terms:
-6.5 + x = -5.809475019

Solving
-6.5 + x = -5.809475019

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -5.809475019 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -5.809475019 + 6.5
x = -5.809475019 + 6.5

Combine like terms: -5.809475019 + 6.5 = 0.690524981
x = 0.690524981

Simplifying
x = 0.690524981

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.309475019, 0.690524981}