-21=2(x-8)3x

Solution for -21=2(x-8)3x equation:

Simplifying
-21 = 2(x + -8) * 3x

Reorder the terms:
-21 = 2(-8 + x) * 3x

Reorder the terms for easier multiplication:
-21 = 2 * 3x(-8 + x)

Multiply 2 * 3
-21 = 6x(-8 + x)
-21 = (-8 * 6x + x * 6x)
-21 = (-48x + 6x2)

Solving
-21 = -48x + 6x2

Solving for variable 'x'.

Reorder the terms:
-21 + 48x + -6x2 = -48x + 48x + 6x2 + -6x2

Combine like terms: -48x + 48x = 0
-21 + 48x + -6x2 = 0 + 6x2 + -6x2
-21 + 48x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-21 + 48x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 16x + -2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 16x + -2x2)' equal to zero and attempt to solve:

Simplifying
-7 + 16x + -2x2 = 0

Solving
-7 + 16x + -2x2 = 0

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

Divide each side by '-2'.
3.5 + -8x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -8x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -8x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -8x + x2 = 0 + -3.5
-8x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-8x + x2 = -3.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -3.5 + 16

Reorder the terms:
16 + -8x + x2 = -3.5 + 16

Combine like terms: -3.5 + 16 = 12.5
16 + -8x + x2 = 12.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + -4) equal to 3.535533906 and -3.535533906.

Subproblem 1
x + -4 = 3.535533906

Simplifying
x + -4 = 3.535533906

Reorder the terms:
-4 + x = 3.535533906

Solving
-4 + x = 3.535533906

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.535533906 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.535533906 + 4
x = 3.535533906 + 4

Combine like terms: 3.535533906 + 4 = 7.535533906
x = 7.535533906

Simplifying
x = 7.535533906

Subproblem 2
x + -4 = -3.535533906

Simplifying
x + -4 = -3.535533906

Reorder the terms:
-4 + x = -3.535533906

Solving
-4 + x = -3.535533906

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.535533906 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.535533906 + 4
x = -3.535533906 + 4

Combine like terms: -3.535533906 + 4 = 0.464466094
x = 0.464466094

Simplifying
x = 0.464466094

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.535533906, 0.464466094}
Solution
x = {7.535533906, 0.464466094}