3x(2-x)=x-3

Solution for 3x(2-x)=x-3 equation:

Simplifying
3x(2 + -1x) = x + -3
(2 * 3x + -1x * 3x) = x + -3
(6x + -3x2) = x + -3

Reorder the terms:
6x + -3x2 = -3 + x

Solving
6x + -3x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
3 + 6x + -1x + -3x2 = -3 + x + 3 + -1x

Combine like terms: 6x + -1x = 5x
3 + 5x + -3x2 = -3 + x + 3 + -1x

Reorder the terms:
3 + 5x + -3x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
3 + 5x + -3x2 = 0 + x + -1x
3 + 5x + -3x2 = x + -1x

Combine like terms: x + -1x = 0
3 + 5x + -3x2 = 0

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

Divide each side by '-3'.
-1 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.666666667x + x2 = 0 + 1
-1.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.666666667x + x2 = 1

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + -1.666666667x + x2 = 1.6944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1
x + -0.8333333335 = 1.301708279

Simplifying
x + -0.8333333335 = 1.301708279

Reorder the terms:
-0.8333333335 + x = 1.301708279

Solving
-0.8333333335 + x = 1.301708279

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.301708279 + 0.8333333335
x = 1.301708279 + 0.8333333335

Combine like terms: 1.301708279 + 0.8333333335 = 2.1350416125
x = 2.1350416125

Simplifying
x = 2.1350416125

Subproblem 2
x + -0.8333333335 = -1.301708279

Simplifying
x + -0.8333333335 = -1.301708279

Reorder the terms:
-0.8333333335 + x = -1.301708279

Solving
-0.8333333335 + x = -1.301708279

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.301708279 + 0.8333333335
x = -1.301708279 + 0.8333333335

Combine like terms: -1.301708279 + 0.8333333335 = -0.4683749455
x = -0.4683749455

Simplifying
x = -0.4683749455

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1350416125, -0.4683749455}