14(x-4)-(x-2)=(x+2)(x-4)

Solution for 14(x-4)-(x-2)=(x+2)(x-4) equation:

Simplifying
14(x + -4) + -1(x + -2) = (x + 2)(x + -4)

Reorder the terms:
14(-4 + x) + -1(x + -2) = (x + 2)(x + -4)
(-4 * 14 + x * 14) + -1(x + -2) = (x + 2)(x + -4)
(-56 + 14x) + -1(x + -2) = (x + 2)(x + -4)

Reorder the terms:
-56 + 14x + -1(-2 + x) = (x + 2)(x + -4)
-56 + 14x + (-2 * -1 + x * -1) = (x + 2)(x + -4)
-56 + 14x + (2 + -1x) = (x + 2)(x + -4)

Reorder the terms:
-56 + 2 + 14x + -1x = (x + 2)(x + -4)

Combine like terms: -56 + 2 = -54
-54 + 14x + -1x = (x + 2)(x + -4)

Combine like terms: 14x + -1x = 13x
-54 + 13x = (x + 2)(x + -4)

Reorder the terms:
-54 + 13x = (2 + x)(x + -4)

Reorder the terms:
-54 + 13x = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-54 + 13x = (2(-4 + x) + x(-4 + x))
-54 + 13x = ((-4 * 2 + x * 2) + x(-4 + x))
-54 + 13x = ((-8 + 2x) + x(-4 + x))
-54 + 13x = (-8 + 2x + (-4 * x + x * x))
-54 + 13x = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-54 + 13x = (-8 + -2x + x2)

Solving
-54 + 13x = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-54 + 8 + 13x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -54 + 8 = -46
-46 + 13x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 13x + 2x = 15x
-46 + 15x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
-46 + 15x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
-46 + 15x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-46 + 15x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-46 + 15x + -1x2 = 0 + x2 + -1x2
-46 + 15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-46 + 15x + -1x2 = 0

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

Divide each side by '-1'.
46 + -15x + x2 = 0

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -15x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -15x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -15x + x2 = 0 + -46
-15x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-15x + x2 = -46

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -46 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -46 + 56.25

Combine like terms: -46 + 56.25 = 10.25
56.25 + -15x + x2 = 10.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -7.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + -7.5 = 3.201562119

Simplifying
x + -7.5 = 3.201562119

Reorder the terms:
-7.5 + x = 3.201562119

Solving
-7.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 3.201562119 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 3.201562119 + 7.5
x = 3.201562119 + 7.5

Combine like terms: 3.201562119 + 7.5 = 10.701562119
x = 10.701562119

Simplifying
x = 10.701562119

Subproblem 2
x + -7.5 = -3.201562119

Simplifying
x + -7.5 = -3.201562119

Reorder the terms:
-7.5 + x = -3.201562119

Solving
-7.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -3.201562119 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -3.201562119 + 7.5
x = -3.201562119 + 7.5

Combine like terms: -3.201562119 + 7.5 = 4.298437881
x = 4.298437881

Simplifying
x = 4.298437881

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.701562119, 4.298437881}