46=2(x-21)3x

Solution for 46=2(x-21)3x equation:

Simplifying
46 = 2(x + -21) * 3x

Reorder the terms:
46 = 2(-21 + x) * 3x

Reorder the terms for easier multiplication:
46 = 2 * 3x(-21 + x)

Multiply 2 * 3
46 = 6x(-21 + x)
46 = (-21 * 6x + x * 6x)
46 = (-126x + 6x2)

Solving
46 = -126x + 6x2

Solving for variable 'x'.

Reorder the terms:
46 + 126x + -6x2 = -126x + 126x + 6x2 + -6x2

Combine like terms: -126x + 126x = 0
46 + 126x + -6x2 = 0 + 6x2 + -6x2
46 + 126x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
46 + 126x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 63x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(23 + 63x + -3x2)' equal to zero and attempt to solve:

Simplifying
23 + 63x + -3x2 = 0

Solving
23 + 63x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-7.666666667 + -21x + x2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + -21x + 7.666666667 + x2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + -21x + x2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + -21x + x2 = 0 + 7.666666667
-21x + x2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
-21x + x2 = 7.666666667

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 = 7.666666667 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 7.666666667 + 110.25

Combine like terms: 7.666666667 + 110.25 = 117.916666667
110.25 + -21x + x2 = 117.916666667

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 117.916666667

Calculate the square root of the right side: 10.858944086

Break this problem into two subproblems by setting 
(x + -10.5) equal to 10.858944086 and -10.858944086.

Subproblem 1
x + -10.5 = 10.858944086

Simplifying
x + -10.5 = 10.858944086

Reorder the terms:
-10.5 + x = 10.858944086

Solving
-10.5 + x = 10.858944086

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 = 10.858944086 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 10.858944086 + 10.5
x = 10.858944086 + 10.5

Combine like terms: 10.858944086 + 10.5 = 21.358944086
x = 21.358944086

Simplifying
x = 21.358944086

Subproblem 2
x + -10.5 = -10.858944086

Simplifying
x + -10.5 = -10.858944086

Reorder the terms:
-10.5 + x = -10.858944086

Solving
-10.5 + x = -10.858944086

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 = -10.858944086 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -10.858944086 + 10.5
x = -10.858944086 + 10.5

Combine like terms: -10.858944086 + 10.5 = -0.358944086
x = -0.358944086

Simplifying
x = -0.358944086

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.358944086, -0.358944086}
Solution
x = {21.358944086, -0.358944086}