x=-2(x-3)(x-8)

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

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

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

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

Multiply (-3 + x) * (-8 + x)
x = -2(-3(-8 + x) + x(-8 + x))
x = -2((-8 * -3 + x * -3) + x(-8 + x))
x = -2((24 + -3x) + x(-8 + x))
x = -2(24 + -3x + (-8 * x + x * x))
x = -2(24 + -3x + (-8x + x2))

Combine like terms: -3x + -8x = -11x
x = -2(24 + -11x + x2)
x = (24 * -2 + -11x * -2 + x2 * -2)
x = (-48 + 22x + -2x2)

Solving
x = -48 + 22x + -2x2

Solving for variable 'x'.

Reorder the terms:
48 + x + -22x + 2x2 = -48 + 22x + -2x2 + 48 + -22x + 2x2

Combine like terms: x + -22x = -21x
48 + -21x + 2x2 = -48 + 22x + -2x2 + 48 + -22x + 2x2

Reorder the terms:
48 + -21x + 2x2 = -48 + 48 + 22x + -22x + -2x2 + 2x2

Combine like terms: -48 + 48 = 0
48 + -21x + 2x2 = 0 + 22x + -22x + -2x2 + 2x2
48 + -21x + 2x2 = 22x + -22x + -2x2 + 2x2

Combine like terms: 22x + -22x = 0
48 + -21x + 2x2 = 0 + -2x2 + 2x2
48 + -21x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
48 + -21x + 2x2 = 0

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

Divide each side by '2'.
24 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -10.5x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -10.5x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -10.5x + x2 = 0 + -24
-10.5x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-10.5x + x2 = -24

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -24 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -24 + 27.5625

Combine like terms: -24 + 27.5625 = 3.5625
27.5625 + -10.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -5.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
x + -5.25 = 1.887458609

Simplifying
x + -5.25 = 1.887458609

Reorder the terms:
-5.25 + x = 1.887458609

Solving
-5.25 + x = 1.887458609

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 1.887458609 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 1.887458609 + 5.25
x = 1.887458609 + 5.25

Combine like terms: 1.887458609 + 5.25 = 7.137458609
x = 7.137458609

Simplifying
x = 7.137458609

Subproblem 2
x + -5.25 = -1.887458609

Simplifying
x + -5.25 = -1.887458609

Reorder the terms:
-5.25 + x = -1.887458609

Solving
-5.25 + x = -1.887458609

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -1.887458609 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -1.887458609 + 5.25
x = -1.887458609 + 5.25

Combine like terms: -1.887458609 + 5.25 = 3.362541391
x = 3.362541391

Simplifying
x = 3.362541391

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.137458609, 3.362541391}