2(x-2)6(2-8x)+5=

Solution for 2(x-2)6(2-8x)+5= equation:

Simplifying
2(x + -2) * 6(2 + -8x) + 5 = 0

Reorder the terms:
2(-2 + x) * 6(2 + -8x) + 5 = 0

Reorder the terms for easier multiplication:
2 * 6(-2 + x)(2 + -8x) + 5 = 0

Multiply 2 * 6
12(-2 + x)(2 + -8x) + 5 = 0

Multiply (-2 + x) * (2 + -8x)
12(-2(2 + -8x) + x(2 + -8x)) + 5 = 0
12((2 * -2 + -8x * -2) + x(2 + -8x)) + 5 = 0
12((-4 + 16x) + x(2 + -8x)) + 5 = 0
12(-4 + 16x + (2 * x + -8x * x)) + 5 = 0
12(-4 + 16x + (2x + -8x2)) + 5 = 0

Combine like terms: 16x + 2x = 18x
12(-4 + 18x + -8x2) + 5 = 0
(-4 * 12 + 18x * 12 + -8x2 * 12) + 5 = 0
(-48 + 216x + -96x2) + 5 = 0

Reorder the terms:
-48 + 5 + 216x + -96x2 = 0

Combine like terms: -48 + 5 = -43
-43 + 216x + -96x2 = 0

Solving
-43 + 216x + -96x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-96 the coefficient of the squared term: 

Divide each side by '-96'.
0.4479166667 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.4479166667' to each side of the equation.
0.4479166667 + -2.25x + -0.4479166667 + x2 = 0 + -0.4479166667

Reorder the terms:
0.4479166667 + -0.4479166667 + -2.25x + x2 = 0 + -0.4479166667

Combine like terms: 0.4479166667 + -0.4479166667 = 0.0000000000
0.0000000000 + -2.25x + x2 = 0 + -0.4479166667
-2.25x + x2 = 0 + -0.4479166667

Combine like terms: 0 + -0.4479166667 = -0.4479166667
-2.25x + x2 = -0.4479166667

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.4479166667 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.4479166667 + 1.265625

Combine like terms: -0.4479166667 + 1.265625 = 0.8177083333
1.265625 + -2.25x + x2 = 0.8177083333

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.8177083333

Calculate the square root of the right side: 0.904272267

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.904272267 and -0.904272267.

Subproblem 1
x + -1.125 = 0.904272267

Simplifying
x + -1.125 = 0.904272267

Reorder the terms:
-1.125 + x = 0.904272267

Solving
-1.125 + x = 0.904272267

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.904272267 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.904272267 + 1.125
x = 0.904272267 + 1.125

Combine like terms: 0.904272267 + 1.125 = 2.029272267
x = 2.029272267

Simplifying
x = 2.029272267

Subproblem 2
x + -1.125 = -0.904272267

Simplifying
x + -1.125 = -0.904272267

Reorder the terms:
-1.125 + x = -0.904272267

Solving
-1.125 + x = -0.904272267

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.904272267 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.904272267 + 1.125
x = -0.904272267 + 1.125

Combine like terms: -0.904272267 + 1.125 = 0.220727733
x = 0.220727733

Simplifying
x = 0.220727733

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.029272267, 0.220727733}