x+8x(x-1)=5(x+2)

Solution for x+8x(x-1)=5(x+2) equation:

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

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

Combine like terms: x + -8x = -7x
-7x + 8x2 = 5(x + 2)

Reorder the terms:
-7x + 8x2 = 5(2 + x)
-7x + 8x2 = (2 * 5 + x * 5)
-7x + 8x2 = (10 + 5x)

Solving
-7x + 8x2 = 10 + 5x

Solving for variable 'x'.

Reorder the terms:
-10 + -7x + -5x + 8x2 = 10 + 5x + -10 + -5x

Combine like terms: -7x + -5x = -12x
-10 + -12x + 8x2 = 10 + 5x + -10 + -5x

Reorder the terms:
-10 + -12x + 8x2 = 10 + -10 + 5x + -5x

Combine like terms: 10 + -10 = 0
-10 + -12x + 8x2 = 0 + 5x + -5x
-10 + -12x + 8x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-10 + -12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -6x + 4x2 = 0

Solving
-5 + -6x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.5x + x2 = 0 + 1.25
-1.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.5x + x2 = 1.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.25 + 0.5625

Combine like terms: 1.25 + 0.5625 = 1.8125
0.5625 + -1.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.346291202 and -1.346291202.

Subproblem 1
x + -0.75 = 1.346291202

Simplifying
x + -0.75 = 1.346291202

Reorder the terms:
-0.75 + x = 1.346291202

Solving
-0.75 + x = 1.346291202

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.346291202 + 0.75
x = 1.346291202 + 0.75

Combine like terms: 1.346291202 + 0.75 = 2.096291202
x = 2.096291202

Simplifying
x = 2.096291202

Subproblem 2
x + -0.75 = -1.346291202

Simplifying
x + -0.75 = -1.346291202

Reorder the terms:
-0.75 + x = -1.346291202

Solving
-0.75 + x = -1.346291202

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.346291202 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.346291202 + 0.75
x = -1.346291202 + 0.75

Combine like terms: -1.346291202 + 0.75 = -0.596291202
x = -0.596291202

Simplifying
x = -0.596291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.096291202, -0.596291202}
Solution
x = {2.096291202, -0.596291202}