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

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


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

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

Reorder the terms:
8 + 2x = 8x(-5 + x)
8 + 2x = (-5 * 8x + x * 8x)
8 + 2x = (-40x + 8x2)

Solving
8 + 2x = -40x + 8x2

Solving for variable 'x'.

Combine like terms: 2x + 40x = 42x
8 + 42x + -8x2 = -40x + 8x2 + 40x + -8x2

Reorder the terms:
8 + 42x + -8x2 = -40x + 40x + 8x2 + -8x2

Combine like terms: -40x + 40x = 0
8 + 42x + -8x2 = 0 + 8x2 + -8x2
8 + 42x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
8 + 42x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 21x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 21x + -4x2)' equal to zero and attempt to solve:

Simplifying
4 + 21x + -4x2 = 0

Solving
4 + 21x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1 + -5.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -5.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5.25x + x2 = 0 + 1
-5.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5.25x + x2 = 1

The x term is -5.25x.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25x + 6.890625 + x2 = 1 + 6.890625

Reorder the terms:
6.890625 + -5.25x + x2 = 1 + 6.890625

Combine like terms: 1 + 6.890625 = 7.890625
6.890625 + -5.25x + x2 = 7.890625

Factor a perfect square on the left side:
(x + -2.625)(x + -2.625) = 7.890625

Calculate the square root of the right side: 2.809025632

Break this problem into two subproblems by setting 
(x + -2.625) equal to 2.809025632 and -2.809025632.


Subproblem 1
x + -2.625 = 2.809025632

Simplifying
x + -2.625 = 2.809025632

Reorder the terms:
-2.625 + x = 2.809025632

Solving
-2.625 + x = 2.809025632

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = 2.809025632 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = 2.809025632 + 2.625
x = 2.809025632 + 2.625

Combine like terms: 2.809025632 + 2.625 = 5.434025632
x = 5.434025632

Simplifying
x = 5.434025632


Subproblem 2
x + -2.625 = -2.809025632

Simplifying
x + -2.625 = -2.809025632

Reorder the terms:
-2.625 + x = -2.809025632

Solving
-2.625 + x = -2.809025632

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = -2.809025632 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = -2.809025632 + 2.625
x = -2.809025632 + 2.625

Combine like terms: -2.809025632 + 2.625 = -0.184025632
x = -0.184025632

Simplifying
x = -0.184025632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.434025632, -0.184025632}
Solution
x = {5.434025632, -0.184025632}

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