21(2-x)12x=44

Solution for 21(2-x)12x=44 equation:

Simplifying
21(2 + -1x) * 12x = 44

Reorder the terms for easier multiplication:
21 * 12x(2 + -1x) = 44

Multiply 21 * 12
252x(2 + -1x) = 44
(2 * 252x + -1x * 252x) = 44
(504x + -252x2) = 44

Solving
504x + -252x2 = 44

Solving for variable 'x'.

Reorder the terms:
-44 + 504x + -252x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-44 + 504x + -252x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + 126x + -63x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + 126x + -63x2)' equal to zero and attempt to solve:

Simplifying
-11 + 126x + -63x2 = 0

Solving
-11 + 126x + -63x2 = 0

Begin completing the square.  Divide all terms by
-63 the coefficient of the squared term: 

Divide each side by '-63'.
0.1746031746 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.1746031746' to each side of the equation.
0.1746031746 + -2x + -0.1746031746 + x2 = 0 + -0.1746031746

Reorder the terms:
0.1746031746 + -0.1746031746 + -2x + x2 = 0 + -0.1746031746

Combine like terms: 0.1746031746 + -0.1746031746 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.1746031746
-2x + x2 = 0 + -0.1746031746

Combine like terms: 0 + -0.1746031746 = -0.1746031746
-2x + x2 = -0.1746031746

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.1746031746 + 1

Reorder the terms:
1 + -2x + x2 = -0.1746031746 + 1

Combine like terms: -0.1746031746 + 1 = 0.8253968254
1 + -2x + x2 = 0.8253968254

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.8253968254

Calculate the square root of the right side: 0.908513525

Break this problem into two subproblems by setting 
(x + -1) equal to 0.908513525 and -0.908513525.

Subproblem 1
x + -1 = 0.908513525

Simplifying
x + -1 = 0.908513525

Reorder the terms:
-1 + x = 0.908513525

Solving
-1 + x = 0.908513525

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.908513525 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.908513525 + 1
x = 0.908513525 + 1

Combine like terms: 0.908513525 + 1 = 1.908513525
x = 1.908513525

Simplifying
x = 1.908513525

Subproblem 2
x + -1 = -0.908513525

Simplifying
x + -1 = -0.908513525

Reorder the terms:
-1 + x = -0.908513525

Solving
-1 + x = -0.908513525

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.908513525 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.908513525 + 1
x = -0.908513525 + 1

Combine like terms: -0.908513525 + 1 = 0.091486475
x = 0.091486475

Simplifying
x = 0.091486475

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.908513525, 0.091486475}
Solution
x = {1.908513525, 0.091486475}