2(x-3)+9=3(x+1)x

Solution for 2(x-3)+9=3(x+1)x equation:

Simplifying
2(x + -3) + 9 = 3(x + 1) * x

Reorder the terms:
2(-3 + x) + 9 = 3(x + 1) * x
(-3 * 2 + x * 2) + 9 = 3(x + 1) * x
(-6 + 2x) + 9 = 3(x + 1) * x

Reorder the terms:
-6 + 9 + 2x = 3(x + 1) * x

Combine like terms: -6 + 9 = 3
3 + 2x = 3(x + 1) * x

Reorder the terms:
3 + 2x = 3(1 + x) * x

Reorder the terms for easier multiplication:
3 + 2x = 3x(1 + x)
3 + 2x = (1 * 3x + x * 3x)
3 + 2x = (3x + 3x2)

Solving
3 + 2x = 3x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + -3x = -1x
3 + -1x + -3x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
3 + -1x + -3x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
3 + -1x + -3x2 = 0 + 3x2 + -3x2
3 + -1x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
3 + -1x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333x + x2 = 0 + 1
0.3333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333x + x2 = 1

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + 0.3333333333x + x2 = 1.02777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1
x + 0.1666666667 = 1.013793755

Simplifying
x + 0.1666666667 = 1.013793755

Reorder the terms:
0.1666666667 + x = 1.013793755

Solving
0.1666666667 + x = 1.013793755

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 1.013793755 + -0.1666666667
x = 1.013793755 + -0.1666666667

Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883
x = 0.8471270883

Simplifying
x = 0.8471270883

Subproblem 2
x + 0.1666666667 = -1.013793755

Simplifying
x + 0.1666666667 = -1.013793755

Reorder the terms:
0.1666666667 + x = -1.013793755

Solving
0.1666666667 + x = -1.013793755

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -1.013793755 + -0.1666666667
x = -1.013793755 + -0.1666666667

Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217
x = -1.1804604217

Simplifying
x = -1.1804604217

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8471270883, -1.1804604217}