1008=(2x-8)(x+8)

Solution for 1008=(2x-8)(x+8) equation:

Simplifying
1008 = (2x + -8)(x + 8)

Reorder the terms:
1008 = (-8 + 2x)(x + 8)

Reorder the terms:
1008 = (-8 + 2x)(8 + x)

Multiply (-8 + 2x) * (8 + x)
1008 = (-8(8 + x) + 2x * (8 + x))
1008 = ((8 * -8 + x * -8) + 2x * (8 + x))
1008 = ((-64 + -8x) + 2x * (8 + x))
1008 = (-64 + -8x + (8 * 2x + x * 2x))
1008 = (-64 + -8x + (16x + 2x2))

Combine like terms: -8x + 16x = 8x
1008 = (-64 + 8x + 2x2)

Solving
1008 = -64 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 1008 + 64 = 1072
1072 + -8x + -2x2 = -64 + 8x + 2x2 + 64 + -8x + -2x2

Reorder the terms:
1072 + -8x + -2x2 = -64 + 64 + 8x + -8x + 2x2 + -2x2

Combine like terms: -64 + 64 = 0
1072 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
1072 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
1072 + -8x + -2x2 = 0 + 2x2 + -2x2
1072 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1072 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(536 + -4x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(536 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
536 + -4x + -1x2 = 0

Solving
536 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-536 + 4x + x2 = 0

Move the constant term to the right:

Add '536' to each side of the equation.
-536 + 4x + 536 + x2 = 0 + 536

Reorder the terms:
-536 + 536 + 4x + x2 = 0 + 536

Combine like terms: -536 + 536 = 0
0 + 4x + x2 = 0 + 536
4x + x2 = 0 + 536

Combine like terms: 0 + 536 = 536
4x + x2 = 536

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 536 + 4

Reorder the terms:
4 + 4x + x2 = 536 + 4

Combine like terms: 536 + 4 = 540
4 + 4x + x2 = 540

Factor a perfect square on the left side:
(x + 2)(x + 2) = 540

Calculate the square root of the right side: 23.237900077

Break this problem into two subproblems by setting 
(x + 2) equal to 23.237900077 and -23.237900077.

Subproblem 1
x + 2 = 23.237900077

Simplifying
x + 2 = 23.237900077

Reorder the terms:
2 + x = 23.237900077

Solving
2 + x = 23.237900077

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 23.237900077 + -2

Combine like terms: 2 + -2 = 0
0 + x = 23.237900077 + -2
x = 23.237900077 + -2

Combine like terms: 23.237900077 + -2 = 21.237900077
x = 21.237900077

Simplifying
x = 21.237900077

Subproblem 2
x + 2 = -23.237900077

Simplifying
x + 2 = -23.237900077

Reorder the terms:
2 + x = -23.237900077

Solving
2 + x = -23.237900077

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -23.237900077 + -2

Combine like terms: 2 + -2 = 0
0 + x = -23.237900077 + -2
x = -23.237900077 + -2

Combine like terms: -23.237900077 + -2 = -25.237900077
x = -25.237900077

Simplifying
x = -25.237900077

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.237900077, -25.237900077}
Solution
x = {21.237900077, -25.237900077}