(2-x)(12+4x)=(-4-2x)(24-2x)

Solution for (2-x)(12+4x)=(-4-2x)(24-2x) equation:

Simplifying
(2 + -1x)(12 + 4x) = (-4 + -2x)(24 + -2x)

Multiply (2 + -1x) * (12 + 4x)
(2(12 + 4x) + -1x * (12 + 4x)) = (-4 + -2x)(24 + -2x)
((12 * 2 + 4x * 2) + -1x * (12 + 4x)) = (-4 + -2x)(24 + -2x)
((24 + 8x) + -1x * (12 + 4x)) = (-4 + -2x)(24 + -2x)
(24 + 8x + (12 * -1x + 4x * -1x)) = (-4 + -2x)(24 + -2x)
(24 + 8x + (-12x + -4x2)) = (-4 + -2x)(24 + -2x)

Combine like terms: 8x + -12x = -4x
(24 + -4x + -4x2) = (-4 + -2x)(24 + -2x)

Multiply (-4 + -2x) * (24 + -2x)
24 + -4x + -4x2 = (-4(24 + -2x) + -2x * (24 + -2x))
24 + -4x + -4x2 = ((24 * -4 + -2x * -4) + -2x * (24 + -2x))
24 + -4x + -4x2 = ((-96 + 8x) + -2x * (24 + -2x))
24 + -4x + -4x2 = (-96 + 8x + (24 * -2x + -2x * -2x))
24 + -4x + -4x2 = (-96 + 8x + (-48x + 4x2))

Combine like terms: 8x + -48x = -40x
24 + -4x + -4x2 = (-96 + -40x + 4x2)

Solving
24 + -4x + -4x2 = -96 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
24 + 96 + -4x + 40x + -4x2 + -4x2 = -96 + -40x + 4x2 + 96 + 40x + -4x2

Combine like terms: 24 + 96 = 120
120 + -4x + 40x + -4x2 + -4x2 = -96 + -40x + 4x2 + 96 + 40x + -4x2

Combine like terms: -4x + 40x = 36x
120 + 36x + -4x2 + -4x2 = -96 + -40x + 4x2 + 96 + 40x + -4x2

Combine like terms: -4x2 + -4x2 = -8x2
120 + 36x + -8x2 = -96 + -40x + 4x2 + 96 + 40x + -4x2

Reorder the terms:
120 + 36x + -8x2 = -96 + 96 + -40x + 40x + 4x2 + -4x2

Combine like terms: -96 + 96 = 0
120 + 36x + -8x2 = 0 + -40x + 40x + 4x2 + -4x2
120 + 36x + -8x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
120 + 36x + -8x2 = 0 + 4x2 + -4x2
120 + 36x + -8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
120 + 36x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 9x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(30 + 9x + -2x2)' equal to zero and attempt to solve:

Simplifying
30 + 9x + -2x2 = 0

Solving
30 + 9x + -2x2 = 0

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

Divide each side by '-2'.
-15 + -4.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -4.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -4.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4.5x + x2 = 0 + 15
-4.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-4.5x + x2 = 15

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 15 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 15 + 5.0625

Combine like terms: 15 + 5.0625 = 20.0625
5.0625 + -4.5x + x2 = 20.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 20.0625

Calculate the square root of the right side: 4.479118217

Break this problem into two subproblems by setting 
(x + -2.25) equal to 4.479118217 and -4.479118217.

Subproblem 1
x + -2.25 = 4.479118217

Simplifying
x + -2.25 = 4.479118217

Reorder the terms:
-2.25 + x = 4.479118217

Solving
-2.25 + x = 4.479118217

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 4.479118217 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 4.479118217 + 2.25
x = 4.479118217 + 2.25

Combine like terms: 4.479118217 + 2.25 = 6.729118217
x = 6.729118217

Simplifying
x = 6.729118217

Subproblem 2
x + -2.25 = -4.479118217

Simplifying
x + -2.25 = -4.479118217

Reorder the terms:
-2.25 + x = -4.479118217

Solving
-2.25 + x = -4.479118217

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -4.479118217 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -4.479118217 + 2.25
x = -4.479118217 + 2.25

Combine like terms: -4.479118217 + 2.25 = -2.229118217
x = -2.229118217

Simplifying
x = -2.229118217

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.729118217, -2.229118217}
Solution
x = {6.729118217, -2.229118217}