8x+4=8x(x+9)

Solution for 8x+4=8x(x+9) equation:

Simplifying
8x + 4 = 8x(x + 9)

Reorder the terms:
4 + 8x = 8x(x + 9)

Reorder the terms:
4 + 8x = 8x(9 + x)
4 + 8x = (9 * 8x + x * 8x)
4 + 8x = (72x + 8x2)

Solving
4 + 8x = 72x + 8x2

Solving for variable 'x'.

Combine like terms: 8x + -72x = -64x
4 + -64x + -8x2 = 72x + 8x2 + -72x + -8x2

Reorder the terms:
4 + -64x + -8x2 = 72x + -72x + 8x2 + -8x2

Combine like terms: 72x + -72x = 0
4 + -64x + -8x2 = 0 + 8x2 + -8x2
4 + -64x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
4 + -64x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -16x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -16x + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -16x + -2x2 = 0

Solving
1 + -16x + -2x2 = 0

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

Divide each side by '-2'.
-0.5 + 8x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 8x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 8x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 8x + x2 = 0 + 0.5
8x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
8x + x2 = 0.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 0.5 + 16

Reorder the terms:
16 + 8x + x2 = 0.5 + 16

Combine like terms: 0.5 + 16 = 16.5
16 + 8x + x2 = 16.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 16.5

Calculate the square root of the right side: 4.062019202

Break this problem into two subproblems by setting 
(x + 4) equal to 4.062019202 and -4.062019202.

Subproblem 1
x + 4 = 4.062019202

Simplifying
x + 4 = 4.062019202

Reorder the terms:
4 + x = 4.062019202

Solving
4 + x = 4.062019202

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.062019202 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.062019202 + -4
x = 4.062019202 + -4

Combine like terms: 4.062019202 + -4 = 0.062019202
x = 0.062019202

Simplifying
x = 0.062019202

Subproblem 2
x + 4 = -4.062019202

Simplifying
x + 4 = -4.062019202

Reorder the terms:
4 + x = -4.062019202

Solving
4 + x = -4.062019202

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.062019202 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.062019202 + -4
x = -4.062019202 + -4

Combine like terms: -4.062019202 + -4 = -8.062019202
x = -8.062019202

Simplifying
x = -8.062019202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.062019202, -8.062019202}
Solution
x = {0.062019202, -8.062019202}