3(x-3)(6-3x)+2x=9(1-x)

Solution for 3(x-3)(6-3x)+2x=9(1-x) equation:

Simplifying
3(x + -3)(6 + -3x) + 2x = 9(1 + -1x)

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

Multiply (-3 + x) * (6 + -3x)
3(-3(6 + -3x) + x(6 + -3x)) + 2x = 9(1 + -1x)
3((6 * -3 + -3x * -3) + x(6 + -3x)) + 2x = 9(1 + -1x)
3((-18 + 9x) + x(6 + -3x)) + 2x = 9(1 + -1x)
3(-18 + 9x + (6 * x + -3x * x)) + 2x = 9(1 + -1x)
3(-18 + 9x + (6x + -3x2)) + 2x = 9(1 + -1x)

Combine like terms: 9x + 6x = 15x
3(-18 + 15x + -3x2) + 2x = 9(1 + -1x)
(-18 * 3 + 15x * 3 + -3x2 * 3) + 2x = 9(1 + -1x)
(-54 + 45x + -9x2) + 2x = 9(1 + -1x)

Reorder the terms:
-54 + 45x + 2x + -9x2 = 9(1 + -1x)

Combine like terms: 45x + 2x = 47x
-54 + 47x + -9x2 = 9(1 + -1x)
-54 + 47x + -9x2 = (1 * 9 + -1x * 9)
-54 + 47x + -9x2 = (9 + -9x)

Solving
-54 + 47x + -9x2 = 9 + -9x

Solving for variable 'x'.

Reorder the terms:
-54 + -9 + 47x + 9x + -9x2 = 9 + -9x + -9 + 9x

Combine like terms: -54 + -9 = -63
-63 + 47x + 9x + -9x2 = 9 + -9x + -9 + 9x

Combine like terms: 47x + 9x = 56x
-63 + 56x + -9x2 = 9 + -9x + -9 + 9x

Reorder the terms:
-63 + 56x + -9x2 = 9 + -9 + -9x + 9x

Combine like terms: 9 + -9 = 0
-63 + 56x + -9x2 = 0 + -9x + 9x
-63 + 56x + -9x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-63 + 56x + -9x2 = 0

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

Divide each side by '-9'.
7 + -6.222222222x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6.222222222x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -6.222222222x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6.222222222x + x2 = 0 + -7
-6.222222222x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6.222222222x + x2 = -7

The x term is -6.222222222x.  Take half its coefficient (-3.111111111).
Square it (9.679012345) and add it to both sides.

Add '9.679012345' to each side of the equation.
-6.222222222x + 9.679012345 + x2 = -7 + 9.679012345

Reorder the terms:
9.679012345 + -6.222222222x + x2 = -7 + 9.679012345

Combine like terms: -7 + 9.679012345 = 2.679012345
9.679012345 + -6.222222222x + x2 = 2.679012345

Factor a perfect square on the left side:
(x + -3.111111111)(x + -3.111111111) = 2.679012345

Calculate the square root of the right side: 1.636768873

Break this problem into two subproblems by setting 
(x + -3.111111111) equal to 1.636768873 and -1.636768873.

Subproblem 1
x + -3.111111111 = 1.636768873

Simplifying
x + -3.111111111 = 1.636768873

Reorder the terms:
-3.111111111 + x = 1.636768873

Solving
-3.111111111 + x = 1.636768873

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = 1.636768873 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = 1.636768873 + 3.111111111
x = 1.636768873 + 3.111111111

Combine like terms: 1.636768873 + 3.111111111 = 4.747879984
x = 4.747879984

Simplifying
x = 4.747879984

Subproblem 2
x + -3.111111111 = -1.636768873

Simplifying
x + -3.111111111 = -1.636768873

Reorder the terms:
-3.111111111 + x = -1.636768873

Solving
-3.111111111 + x = -1.636768873

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = -1.636768873 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = -1.636768873 + 3.111111111
x = -1.636768873 + 3.111111111

Combine like terms: -1.636768873 + 3.111111111 = 1.474342238
x = 1.474342238

Simplifying
x = 1.474342238

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.747879984, 1.474342238}