(x-2)(x+12)=9x

Solution for (x-2)(x+12)=9x equation:

Simplifying
(x + -2)(x + 12) = 9x

Reorder the terms:
(-2 + x)(x + 12) = 9x

Reorder the terms:
(-2 + x)(12 + x) = 9x

Multiply (-2 + x) * (12 + x)
(-2(12 + x) + x(12 + x)) = 9x
((12 * -2 + x * -2) + x(12 + x)) = 9x
((-24 + -2x) + x(12 + x)) = 9x
(-24 + -2x + (12 * x + x * x)) = 9x
(-24 + -2x + (12x + x2)) = 9x

Combine like terms: -2x + 12x = 10x
(-24 + 10x + x2) = 9x

Solving
-24 + 10x + x2 = 9x

Solving for variable 'x'.

Reorder the terms:
-24 + 10x + -9x + x2 = 9x + -9x

Combine like terms: 10x + -9x = 1x
-24 + 1x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-24 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 1x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 1x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 1x + x2 = 0 + 24
1x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
1x + x2 = 24

The x term is 1x.  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.
x + 0.25 + x2 = 24 + 0.25

Reorder the terms:
0.25 + x + x2 = 24 + 0.25

Combine like terms: 24 + 0.25 = 24.25
0.25 + x + x2 = 24.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + 0.5 = 4.924428901

Simplifying
x + 0.5 = 4.924428901

Reorder the terms:
0.5 + x = 4.924428901

Solving
0.5 + x = 4.924428901

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 = 4.924428901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.924428901 + -0.5
x = 4.924428901 + -0.5

Combine like terms: 4.924428901 + -0.5 = 4.424428901
x = 4.424428901

Simplifying
x = 4.424428901

Subproblem 2
x + 0.5 = -4.924428901

Simplifying
x + 0.5 = -4.924428901

Reorder the terms:
0.5 + x = -4.924428901

Solving
0.5 + x = -4.924428901

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 = -4.924428901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.924428901 + -0.5
x = -4.924428901 + -0.5

Combine like terms: -4.924428901 + -0.5 = -5.424428901
x = -5.424428901

Simplifying
x = -5.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.424428901, -5.424428901}