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

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

Simplifying
9x(3 + -1x) = (x + 3)
(3 * 9x + -1x * 9x) = (x + 3)
(27x + -9x2) = (x + 3)

Reorder the terms:
27x + -9x2 = (3 + x)

Remove parenthesis around (3 + x)
27x + -9x2 = 3 + x

Solving
27x + -9x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-3 + 27x + -1x + -9x2 = 3 + x + -3 + -1x

Combine like terms: 27x + -1x = 26x
-3 + 26x + -9x2 = 3 + x + -3 + -1x

Reorder the terms:
-3 + 26x + -9x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-3 + 26x + -9x2 = 0 + x + -1x
-3 + 26x + -9x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + 26x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.3333333333 + -2.888888889x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2.888888889x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2.888888889x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2.888888889x + x2 = 0 + -0.3333333333
-2.888888889x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2.888888889x + x2 = -0.3333333333

The x term is -2.888888889x.  Take half its coefficient (-1.444444445).
Square it (2.086419755) and add it to both sides.

Add '2.086419755' to each side of the equation.
-2.888888889x + 2.086419755 + x2 = -0.3333333333 + 2.086419755

Reorder the terms:
2.086419755 + -2.888888889x + x2 = -0.3333333333 + 2.086419755

Combine like terms: -0.3333333333 + 2.086419755 = 1.7530864217
2.086419755 + -2.888888889x + x2 = 1.7530864217

Factor a perfect square on the left side:
(x + -1.444444445)(x + -1.444444445) = 1.7530864217

Calculate the square root of the right side: 1.324041699

Break this problem into two subproblems by setting 
(x + -1.444444445) equal to 1.324041699 and -1.324041699.

Subproblem 1
x + -1.444444445 = 1.324041699

Simplifying
x + -1.444444445 = 1.324041699

Reorder the terms:
-1.444444445 + x = 1.324041699

Solving
-1.444444445 + x = 1.324041699

Solving for variable 'x'.

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

Add '1.444444445' to each side of the equation.
-1.444444445 + 1.444444445 + x = 1.324041699 + 1.444444445

Combine like terms: -1.444444445 + 1.444444445 = 0.000000000
0.000000000 + x = 1.324041699 + 1.444444445
x = 1.324041699 + 1.444444445

Combine like terms: 1.324041699 + 1.444444445 = 2.768486144
x = 2.768486144

Simplifying
x = 2.768486144

Subproblem 2
x + -1.444444445 = -1.324041699

Simplifying
x + -1.444444445 = -1.324041699

Reorder the terms:
-1.444444445 + x = -1.324041699

Solving
-1.444444445 + x = -1.324041699

Solving for variable 'x'.

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

Add '1.444444445' to each side of the equation.
-1.444444445 + 1.444444445 + x = -1.324041699 + 1.444444445

Combine like terms: -1.444444445 + 1.444444445 = 0.000000000
0.000000000 + x = -1.324041699 + 1.444444445
x = -1.324041699 + 1.444444445

Combine like terms: -1.324041699 + 1.444444445 = 0.120402746
x = 0.120402746

Simplifying
x = 0.120402746

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.768486144, 0.120402746}