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

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

Simplifying
2(6 + -1x) = x(x + 5)
(6 * 2 + -1x * 2) = x(x + 5)
(12 + -2x) = x(x + 5)

Reorder the terms:
12 + -2x = x(5 + x)
12 + -2x = (5 * x + x * x)
12 + -2x = (5x + x2)

Solving
12 + -2x = 5x + x2

Solving for variable 'x'.

Combine like terms: -2x + -5x = -7x
12 + -7x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
12 + -7x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
12 + -7x + -1x2 = 0 + x2 + -1x2
12 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + 7x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 7x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 7x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7x + x2 = 0 + 12
7x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
7x + x2 = 12

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 12 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + 7x + x2 = 24.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + 3.5 = 4.924428901

Simplifying
x + 3.5 = 4.924428901

Reorder the terms:
3.5 + x = 4.924428901

Solving
3.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.924428901 + -3.5
x = 4.924428901 + -3.5

Combine like terms: 4.924428901 + -3.5 = 1.424428901
x = 1.424428901

Simplifying
x = 1.424428901

Subproblem 2
x + 3.5 = -4.924428901

Simplifying
x + 3.5 = -4.924428901

Reorder the terms:
3.5 + x = -4.924428901

Solving
3.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.924428901 + -3.5
x = -4.924428901 + -3.5

Combine like terms: -4.924428901 + -3.5 = -8.424428901
x = -8.424428901

Simplifying
x = -8.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.424428901, -8.424428901}