(3x-4)(x-9)=(x-10)(2x-8)

Solution for (3x-4)(x-9)=(x-10)(2x-8) equation:

Simplifying
(3x + -4)(x + -9) = (x + -10)(2x + -8)

Reorder the terms:
(-4 + 3x)(x + -9) = (x + -10)(2x + -8)

Reorder the terms:
(-4 + 3x)(-9 + x) = (x + -10)(2x + -8)

Multiply (-4 + 3x) * (-9 + x)
(-4(-9 + x) + 3x * (-9 + x)) = (x + -10)(2x + -8)
((-9 * -4 + x * -4) + 3x * (-9 + x)) = (x + -10)(2x + -8)
((36 + -4x) + 3x * (-9 + x)) = (x + -10)(2x + -8)
(36 + -4x + (-9 * 3x + x * 3x)) = (x + -10)(2x + -8)
(36 + -4x + (-27x + 3x2)) = (x + -10)(2x + -8)

Combine like terms: -4x + -27x = -31x
(36 + -31x + 3x2) = (x + -10)(2x + -8)

Reorder the terms:
36 + -31x + 3x2 = (-10 + x)(2x + -8)

Reorder the terms:
36 + -31x + 3x2 = (-10 + x)(-8 + 2x)

Multiply (-10 + x) * (-8 + 2x)
36 + -31x + 3x2 = (-10(-8 + 2x) + x(-8 + 2x))
36 + -31x + 3x2 = ((-8 * -10 + 2x * -10) + x(-8 + 2x))
36 + -31x + 3x2 = ((80 + -20x) + x(-8 + 2x))
36 + -31x + 3x2 = (80 + -20x + (-8 * x + 2x * x))
36 + -31x + 3x2 = (80 + -20x + (-8x + 2x2))

Combine like terms: -20x + -8x = -28x
36 + -31x + 3x2 = (80 + -28x + 2x2)

Solving
36 + -31x + 3x2 = 80 + -28x + 2x2

Solving for variable 'x'.

Reorder the terms:
36 + -80 + -31x + 28x + 3x2 + -2x2 = 80 + -28x + 2x2 + -80 + 28x + -2x2

Combine like terms: 36 + -80 = -44
-44 + -31x + 28x + 3x2 + -2x2 = 80 + -28x + 2x2 + -80 + 28x + -2x2

Combine like terms: -31x + 28x = -3x
-44 + -3x + 3x2 + -2x2 = 80 + -28x + 2x2 + -80 + 28x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-44 + -3x + 1x2 = 80 + -28x + 2x2 + -80 + 28x + -2x2

Reorder the terms:
-44 + -3x + 1x2 = 80 + -80 + -28x + 28x + 2x2 + -2x2

Combine like terms: 80 + -80 = 0
-44 + -3x + 1x2 = 0 + -28x + 28x + 2x2 + -2x2
-44 + -3x + 1x2 = -28x + 28x + 2x2 + -2x2

Combine like terms: -28x + 28x = 0
-44 + -3x + 1x2 = 0 + 2x2 + -2x2
-44 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-44 + -3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -3x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -3x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -3x + x2 = 0 + 44
-3x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-3x + x2 = 44

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 = 44 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 44 + 2.25

Combine like terms: 44 + 2.25 = 46.25
2.25 + -3x + x2 = 46.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + -1.5) equal to 6.800735254 and -6.800735254.

Subproblem 1
x + -1.5 = 6.800735254

Simplifying
x + -1.5 = 6.800735254

Reorder the terms:
-1.5 + x = 6.800735254

Solving
-1.5 + x = 6.800735254

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 = 6.800735254 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 6.800735254 + 1.5
x = 6.800735254 + 1.5

Combine like terms: 6.800735254 + 1.5 = 8.300735254
x = 8.300735254

Simplifying
x = 8.300735254

Subproblem 2
x + -1.5 = -6.800735254

Simplifying
x + -1.5 = -6.800735254

Reorder the terms:
-1.5 + x = -6.800735254

Solving
-1.5 + x = -6.800735254

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 = -6.800735254 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -6.800735254 + 1.5
x = -6.800735254 + 1.5

Combine like terms: -6.800735254 + 1.5 = -5.300735254
x = -5.300735254

Simplifying
x = -5.300735254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.300735254, -5.300735254}