21(2+x)12x=44

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

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

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

Multiply 21 * 12
252x(2 + x) = 44
(2 * 252x + x * 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 = 1.1746031746
1 + 2x + x2 = 1.1746031746

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.1746031746

Calculate the square root of the right side: 1.083791112

Break this problem into two subproblems by setting 
(x + 1) equal to 1.083791112 and -1.083791112.

Subproblem 1
x + 1 = 1.083791112

Simplifying
x + 1 = 1.083791112

Reorder the terms:
1 + x = 1.083791112

Solving
1 + x = 1.083791112

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 = 1.083791112 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.083791112 + -1
x = 1.083791112 + -1

Combine like terms: 1.083791112 + -1 = 0.083791112
x = 0.083791112

Simplifying
x = 0.083791112

Subproblem 2
x + 1 = -1.083791112

Simplifying
x + 1 = -1.083791112

Reorder the terms:
1 + x = -1.083791112

Solving
1 + x = -1.083791112

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 = -1.083791112 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.083791112 + -1
x = -1.083791112 + -1

Combine like terms: -1.083791112 + -1 = -2.083791112
x = -2.083791112

Simplifying
x = -2.083791112

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.083791112, -2.083791112}
Solution
x = {0.083791112, -2.083791112}