5x(x-2)=(x+6)

Solution for 5x(x-2)=(x+6) equation:

Simplifying
5x(x + -2) = (x + 6)

Reorder the terms:
5x(-2 + x) = (x + 6)
(-2 * 5x + x * 5x) = (x + 6)
(-10x + 5x2) = (x + 6)

Reorder the terms:
-10x + 5x2 = (6 + x)

Remove parenthesis around (6 + x)
-10x + 5x2 = 6 + x

Solving
-10x + 5x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-6 + -10x + -1x + 5x2 = 6 + x + -6 + -1x

Combine like terms: -10x + -1x = -11x
-6 + -11x + 5x2 = 6 + x + -6 + -1x

Reorder the terms:
-6 + -11x + 5x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
-6 + -11x + 5x2 = 0 + x + -1x
-6 + -11x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + -11x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -2.2x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.2x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.2x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.2x + x2 = 0 + 1.2
-2.2x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.2x + x2 = 1.2

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 1.2 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 1.2 + 1.21

Combine like terms: 1.2 + 1.21 = 2.41
1.21 + -2.2x + x2 = 2.41

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.55241747 and -1.55241747.

Subproblem 1
x + -1.1 = 1.55241747

Simplifying
x + -1.1 = 1.55241747

Reorder the terms:
-1.1 + x = 1.55241747

Solving
-1.1 + x = 1.55241747

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 1.55241747 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.55241747 + 1.1
x = 1.55241747 + 1.1

Combine like terms: 1.55241747 + 1.1 = 2.65241747
x = 2.65241747

Simplifying
x = 2.65241747

Subproblem 2
x + -1.1 = -1.55241747

Simplifying
x + -1.1 = -1.55241747

Reorder the terms:
-1.1 + x = -1.55241747

Solving
-1.1 + x = -1.55241747

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -1.55241747 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.55241747 + 1.1
x = -1.55241747 + 1.1

Combine like terms: -1.55241747 + 1.1 = -0.45241747
x = -0.45241747

Simplifying
x = -0.45241747

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.65241747, -0.45241747}