(x-4)+(x-3)=(x-2)(3x-16)

Solution for (x-4)+(x-3)=(x-2)(3x-16) equation:

Simplifying
(x + -4) + (x + -3) = (x + -2)(3x + -16)

Reorder the terms:
(-4 + x) + (x + -3) = (x + -2)(3x + -16)

Remove parenthesis around (-4 + x)
-4 + x + (x + -3) = (x + -2)(3x + -16)

Reorder the terms:
-4 + x + (-3 + x) = (x + -2)(3x + -16)

Remove parenthesis around (-3 + x)
-4 + x + -3 + x = (x + -2)(3x + -16)

Reorder the terms:
-4 + -3 + x + x = (x + -2)(3x + -16)

Combine like terms: -4 + -3 = -7
-7 + x + x = (x + -2)(3x + -16)

Combine like terms: x + x = 2x
-7 + 2x = (x + -2)(3x + -16)

Reorder the terms:
-7 + 2x = (-2 + x)(3x + -16)

Reorder the terms:
-7 + 2x = (-2 + x)(-16 + 3x)

Multiply (-2 + x) * (-16 + 3x)
-7 + 2x = (-2(-16 + 3x) + x(-16 + 3x))
-7 + 2x = ((-16 * -2 + 3x * -2) + x(-16 + 3x))
-7 + 2x = ((32 + -6x) + x(-16 + 3x))
-7 + 2x = (32 + -6x + (-16 * x + 3x * x))
-7 + 2x = (32 + -6x + (-16x + 3x2))

Combine like terms: -6x + -16x = -22x
-7 + 2x = (32 + -22x + 3x2)

Solving
-7 + 2x = 32 + -22x + 3x2

Solving for variable 'x'.

Reorder the terms:
-7 + -32 + 2x + 22x + -3x2 = 32 + -22x + 3x2 + -32 + 22x + -3x2

Combine like terms: -7 + -32 = -39
-39 + 2x + 22x + -3x2 = 32 + -22x + 3x2 + -32 + 22x + -3x2

Combine like terms: 2x + 22x = 24x
-39 + 24x + -3x2 = 32 + -22x + 3x2 + -32 + 22x + -3x2

Reorder the terms:
-39 + 24x + -3x2 = 32 + -32 + -22x + 22x + 3x2 + -3x2

Combine like terms: 32 + -32 = 0
-39 + 24x + -3x2 = 0 + -22x + 22x + 3x2 + -3x2
-39 + 24x + -3x2 = -22x + 22x + 3x2 + -3x2

Combine like terms: -22x + 22x = 0
-39 + 24x + -3x2 = 0 + 3x2 + -3x2
-39 + 24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-39 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + 8x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-13 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-13 + 8x + -1x2 = 0

Solving
-13 + 8x + -1x2 = 0

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

Divide each side by '-1'.
13 + -8x + x2 = 0

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -8x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -8x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -8x + x2 = 0 + -13
-8x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-8x + x2 = -13

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -13 + 16

Reorder the terms:
16 + -8x + x2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + -8x + x2 = 3

Factor a perfect square on the left side:
(x + -4)(x + -4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -4) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -4 = 1.732050808

Simplifying
x + -4 = 1.732050808

Reorder the terms:
-4 + x = 1.732050808

Solving
-4 + x = 1.732050808

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = 1.732050808 + 4
x = 1.732050808 + 4

Combine like terms: 1.732050808 + 4 = 5.732050808
x = 5.732050808

Simplifying
x = 5.732050808

Subproblem 2
x + -4 = -1.732050808

Simplifying
x + -4 = -1.732050808

Reorder the terms:
-4 + x = -1.732050808

Solving
-4 + x = -1.732050808

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = -1.732050808 + 4
x = -1.732050808 + 4

Combine like terms: -1.732050808 + 4 = 2.267949192
x = 2.267949192

Simplifying
x = 2.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.732050808, 2.267949192}
Solution
x = {5.732050808, 2.267949192}