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

Solution for 12(x-4)-(x+2)=(x+2)(x+4) equation:

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

Reorder the terms:
12(-4 + x) + -1(x + 2) = (x + 2)(x + 4)
(-4 * 12 + x * 12) + -1(x + 2) = (x + 2)(x + 4)
(-48 + 12x) + -1(x + 2) = (x + 2)(x + 4)

Reorder the terms:
-48 + 12x + -1(2 + x) = (x + 2)(x + 4)
-48 + 12x + (2 * -1 + x * -1) = (x + 2)(x + 4)
-48 + 12x + (-2 + -1x) = (x + 2)(x + 4)

Reorder the terms:
-48 + -2 + 12x + -1x = (x + 2)(x + 4)

Combine like terms: -48 + -2 = -50
-50 + 12x + -1x = (x + 2)(x + 4)

Combine like terms: 12x + -1x = 11x
-50 + 11x = (x + 2)(x + 4)

Reorder the terms:
-50 + 11x = (2 + x)(x + 4)

Reorder the terms:
-50 + 11x = (2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
-50 + 11x = (2(4 + x) + x(4 + x))
-50 + 11x = ((4 * 2 + x * 2) + x(4 + x))
-50 + 11x = ((8 + 2x) + x(4 + x))
-50 + 11x = (8 + 2x + (4 * x + x * x))
-50 + 11x = (8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
-50 + 11x = (8 + 6x + x2)

Solving
-50 + 11x = 8 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-50 + -8 + 11x + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: -50 + -8 = -58
-58 + 11x + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 11x + -6x = 5x
-58 + 5x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
-58 + 5x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-58 + 5x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-58 + 5x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-58 + 5x + -1x2 = 0 + x2 + -1x2
-58 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-58 + 5x + -1x2 = 0

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

Divide each side by '-1'.
58 + -5x + x2 = 0

Move the constant term to the right:

Add '-58' to each side of the equation.
58 + -5x + -58 + x2 = 0 + -58

Reorder the terms:
58 + -58 + -5x + x2 = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -5x + x2 = 0 + -58
-5x + x2 = 0 + -58

Combine like terms: 0 + -58 = -58
-5x + x2 = -58

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -58 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -58 + 6.25

Combine like terms: -58 + 6.25 = -51.75
6.25 + -5x + x2 = -51.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -51.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.