46=2(x-21)2x

Solution for 46=2(x-21)2x equation:

Simplifying
46 = 2(x + -21) * 2x

Reorder the terms:
46 = 2(-21 + x) * 2x

Reorder the terms for easier multiplication:
46 = 2 * 2x(-21 + x)

Multiply 2 * 2
46 = 4x(-21 + x)
46 = (-21 * 4x + x * 4x)
46 = (-84x + 4x2)

Solving
46 = -84x + 4x2

Solving for variable 'x'.

Reorder the terms:
46 + 84x + -4x2 = -84x + 84x + 4x2 + -4x2

Combine like terms: -84x + 84x = 0
46 + 84x + -4x2 = 0 + 4x2 + -4x2
46 + 84x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
46 + 84x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 42x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(23 + 42x + -2x2)' equal to zero and attempt to solve:

Simplifying
23 + 42x + -2x2 = 0

Solving
23 + 42x + -2x2 = 0

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

Divide each side by '-2'.
-11.5 + -21x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -21x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -21x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -21x + x2 = 0 + 11.5
-21x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-21x + x2 = 11.5

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = 11.5 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 11.5 + 110.25

Combine like terms: 11.5 + 110.25 = 121.75
110.25 + -21x + x2 = 121.75

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 121.75

Calculate the square root of the right side: 11.034038245

Break this problem into two subproblems by setting 
(x + -10.5) equal to 11.034038245 and -11.034038245.

Subproblem 1
x + -10.5 = 11.034038245

Simplifying
x + -10.5 = 11.034038245

Reorder the terms:
-10.5 + x = 11.034038245

Solving
-10.5 + x = 11.034038245

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 11.034038245 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 11.034038245 + 10.5
x = 11.034038245 + 10.5

Combine like terms: 11.034038245 + 10.5 = 21.534038245
x = 21.534038245

Simplifying
x = 21.534038245

Subproblem 2
x + -10.5 = -11.034038245

Simplifying
x + -10.5 = -11.034038245

Reorder the terms:
-10.5 + x = -11.034038245

Solving
-10.5 + x = -11.034038245

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -11.034038245 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -11.034038245 + 10.5
x = -11.034038245 + 10.5

Combine like terms: -11.034038245 + 10.5 = -0.534038245
x = -0.534038245

Simplifying
x = -0.534038245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.534038245, -0.534038245}
Solution
x = {21.534038245, -0.534038245}