2-(-x^2+4x+5)=(-2x+4)(8-x)

Solution for 2-(-x^2+4x+5)=(-2x+4)(8-x) equation:

Simplifying
2 + -1(-1x2 + 4x + 5) = (-2x + 4)(8 + -1x)

Reorder the terms:
2 + -1(5 + 4x + -1x2) = (-2x + 4)(8 + -1x)
2 + (5 * -1 + 4x * -1 + -1x2 * -1) = (-2x + 4)(8 + -1x)
2 + (-5 + -4x + 1x2) = (-2x + 4)(8 + -1x)

Combine like terms: 2 + -5 = -3
-3 + -4x + 1x2 = (-2x + 4)(8 + -1x)

Reorder the terms:
-3 + -4x + 1x2 = (4 + -2x)(8 + -1x)

Multiply (4 + -2x) * (8 + -1x)
-3 + -4x + 1x2 = (4(8 + -1x) + -2x * (8 + -1x))
-3 + -4x + 1x2 = ((8 * 4 + -1x * 4) + -2x * (8 + -1x))
-3 + -4x + 1x2 = ((32 + -4x) + -2x * (8 + -1x))
-3 + -4x + 1x2 = (32 + -4x + (8 * -2x + -1x * -2x))
-3 + -4x + 1x2 = (32 + -4x + (-16x + 2x2))

Combine like terms: -4x + -16x = -20x
-3 + -4x + 1x2 = (32 + -20x + 2x2)

Solving
-3 + -4x + 1x2 = 32 + -20x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + -32 + -4x + 20x + 1x2 + -2x2 = 32 + -20x + 2x2 + -32 + 20x + -2x2

Combine like terms: -3 + -32 = -35
-35 + -4x + 20x + 1x2 + -2x2 = 32 + -20x + 2x2 + -32 + 20x + -2x2

Combine like terms: -4x + 20x = 16x
-35 + 16x + 1x2 + -2x2 = 32 + -20x + 2x2 + -32 + 20x + -2x2

Combine like terms: 1x2 + -2x2 = -1x2
-35 + 16x + -1x2 = 32 + -20x + 2x2 + -32 + 20x + -2x2

Reorder the terms:
-35 + 16x + -1x2 = 32 + -32 + -20x + 20x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
-35 + 16x + -1x2 = 0 + -20x + 20x + 2x2 + -2x2
-35 + 16x + -1x2 = -20x + 20x + 2x2 + -2x2

Combine like terms: -20x + 20x = 0
-35 + 16x + -1x2 = 0 + 2x2 + -2x2
-35 + 16x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-35 + 16x + -1x2 = 0

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

Divide each side by '-1'.
35 + -16x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -16x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -16x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -16x + x2 = 0 + -35
-16x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-16x + x2 = -35

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -35 + 64

Reorder the terms:
64 + -16x + x2 = -35 + 64

Combine like terms: -35 + 64 = 29
64 + -16x + x2 = 29

Factor a perfect square on the left side:
(x + -8)(x + -8) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -8) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + -8 = 5.385164807

Simplifying
x + -8 = 5.385164807

Reorder the terms:
-8 + x = 5.385164807

Solving
-8 + x = 5.385164807

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 5.385164807 + 8

Combine like terms: -8 + 8 = 0
0 + x = 5.385164807 + 8
x = 5.385164807 + 8

Combine like terms: 5.385164807 + 8 = 13.385164807
x = 13.385164807

Simplifying
x = 13.385164807

Subproblem 2
x + -8 = -5.385164807

Simplifying
x + -8 = -5.385164807

Reorder the terms:
-8 + x = -5.385164807

Solving
-8 + x = -5.385164807

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -5.385164807 + 8

Combine like terms: -8 + 8 = 0
0 + x = -5.385164807 + 8
x = -5.385164807 + 8

Combine like terms: -5.385164807 + 8 = 2.614835193
x = 2.614835193

Simplifying
x = 2.614835193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.385164807, 2.614835193}