684=(2x-4)(x-4)

Solution for 684=(2x-4)(x-4) equation:

Simplifying
684 = (2x + -4)(x + -4)

Reorder the terms:
684 = (-4 + 2x)(x + -4)

Reorder the terms:
684 = (-4 + 2x)(-4 + x)

Multiply (-4 + 2x) * (-4 + x)
684 = (-4(-4 + x) + 2x * (-4 + x))
684 = ((-4 * -4 + x * -4) + 2x * (-4 + x))
684 = ((16 + -4x) + 2x * (-4 + x))
684 = (16 + -4x + (-4 * 2x + x * 2x))
684 = (16 + -4x + (-8x + 2x2))

Combine like terms: -4x + -8x = -12x
684 = (16 + -12x + 2x2)

Solving
684 = 16 + -12x + 2x2

Solving for variable 'x'.

Combine like terms: 684 + -16 = 668
668 + 12x + -2x2 = 16 + -12x + 2x2 + -16 + 12x + -2x2

Reorder the terms:
668 + 12x + -2x2 = 16 + -16 + -12x + 12x + 2x2 + -2x2

Combine like terms: 16 + -16 = 0
668 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2
668 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
668 + 12x + -2x2 = 0 + 2x2 + -2x2
668 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
668 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(334 + 6x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(334 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
334 + 6x + -1x2 = 0

Solving
334 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-334 + -6x + x2 = 0

Move the constant term to the right:

Add '334' to each side of the equation.
-334 + -6x + 334 + x2 = 0 + 334

Reorder the terms:
-334 + 334 + -6x + x2 = 0 + 334

Combine like terms: -334 + 334 = 0
0 + -6x + x2 = 0 + 334
-6x + x2 = 0 + 334

Combine like terms: 0 + 334 = 334
-6x + x2 = 334

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 334 + 9

Reorder the terms:
9 + -6x + x2 = 334 + 9

Combine like terms: 334 + 9 = 343
9 + -6x + x2 = 343

Factor a perfect square on the left side:
(x + -3)(x + -3) = 343

Calculate the square root of the right side: 18.520259177

Break this problem into two subproblems by setting 
(x + -3) equal to 18.520259177 and -18.520259177.

Subproblem 1
x + -3 = 18.520259177

Simplifying
x + -3 = 18.520259177

Reorder the terms:
-3 + x = 18.520259177

Solving
-3 + x = 18.520259177

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 18.520259177 + 3

Combine like terms: -3 + 3 = 0
0 + x = 18.520259177 + 3
x = 18.520259177 + 3

Combine like terms: 18.520259177 + 3 = 21.520259177
x = 21.520259177

Simplifying
x = 21.520259177

Subproblem 2
x + -3 = -18.520259177

Simplifying
x + -3 = -18.520259177

Reorder the terms:
-3 + x = -18.520259177

Solving
-3 + x = -18.520259177

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -18.520259177 + 3

Combine like terms: -3 + 3 = 0
0 + x = -18.520259177 + 3
x = -18.520259177 + 3

Combine like terms: -18.520259177 + 3 = -15.520259177
x = -15.520259177

Simplifying
x = -15.520259177

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.520259177, -15.520259177}
Solution
x = {21.520259177, -15.520259177}