10x+6=x(10x+8)

Solution for 10x+6=x(10x+8) equation:

Simplifying
10x + 6 = x(10x + 8)

Reorder the terms:
6 + 10x = x(10x + 8)

Reorder the terms:
6 + 10x = x(8 + 10x)
6 + 10x = (8 * x + 10x * x)
6 + 10x = (8x + 10x2)

Solving
6 + 10x = 8x + 10x2

Solving for variable 'x'.

Combine like terms: 10x + -8x = 2x
6 + 2x + -10x2 = 8x + 10x2 + -8x + -10x2

Reorder the terms:
6 + 2x + -10x2 = 8x + -8x + 10x2 + -10x2

Combine like terms: 8x + -8x = 0
6 + 2x + -10x2 = 0 + 10x2 + -10x2
6 + 2x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
6 + 2x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x + -5x2)' equal to zero and attempt to solve:

Simplifying
3 + x + -5x2 = 0

Solving
3 + x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + -0.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.2x + x2 = 0 + 0.6
-0.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.2x + x2 = 0.6

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = 0.6 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + -0.2x + x2 = 0.85

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
x + 0.5 = 0.921954446

Simplifying
x + 0.5 = 0.921954446

Reorder the terms:
0.5 + x = 0.921954446

Solving
0.5 + x = 0.921954446

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.921954446 + -0.5
x = 0.921954446 + -0.5

Combine like terms: 0.921954446 + -0.5 = 0.421954446
x = 0.421954446

Simplifying
x = 0.421954446

Subproblem 2
x + 0.5 = -0.921954446

Simplifying
x + 0.5 = -0.921954446

Reorder the terms:
0.5 + x = -0.921954446

Solving
0.5 + x = -0.921954446

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.921954446 + -0.5
x = -0.921954446 + -0.5

Combine like terms: -0.921954446 + -0.5 = -1.421954446
x = -1.421954446

Simplifying
x = -1.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.421954446, -1.421954446}
Solution
x = {0.421954446, -1.421954446}