2X^2+2(X-3)=3X(X-3)

Solution for 2X^2+2(X-3)=3X(X-3) equation:

Simplifying
2X2 + 2(X + -3) = 3X(X + -3)

Reorder the terms:
2X2 + 2(-3 + X) = 3X(X + -3)
2X2 + (-3 * 2 + X * 2) = 3X(X + -3)
2X2 + (-6 + 2X) = 3X(X + -3)

Reorder the terms:
-6 + 2X + 2X2 = 3X(X + -3)

Reorder the terms:
-6 + 2X + 2X2 = 3X(-3 + X)
-6 + 2X + 2X2 = (-3 * 3X + X * 3X)
-6 + 2X + 2X2 = (-9X + 3X2)

Solving
-6 + 2X + 2X2 = -9X + 3X2

Solving for variable 'X'.

Reorder the terms:
-6 + 2X + 9X + 2X2 + -3X2 = -9X + 3X2 + 9X + -3X2

Combine like terms: 2X + 9X = 11X
-6 + 11X + 2X2 + -3X2 = -9X + 3X2 + 9X + -3X2

Combine like terms: 2X2 + -3X2 = -1X2
-6 + 11X + -1X2 = -9X + 3X2 + 9X + -3X2

Reorder the terms:
-6 + 11X + -1X2 = -9X + 9X + 3X2 + -3X2

Combine like terms: -9X + 9X = 0
-6 + 11X + -1X2 = 0 + 3X2 + -3X2
-6 + 11X + -1X2 = 3X2 + -3X2

Combine like terms: 3X2 + -3X2 = 0
-6 + 11X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -11X + X2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -11X + -6 + X2 = 0 + -6

Reorder the terms:
6 + -6 + -11X + X2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -11X + X2 = 0 + -6
-11X + X2 = 0 + -6

Combine like terms: 0 + -6 = -6
-11X + X2 = -6

The X term is -11X.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11X + 30.25 + X2 = -6 + 30.25

Reorder the terms:
30.25 + -11X + X2 = -6 + 30.25

Combine like terms: -6 + 30.25 = 24.25
30.25 + -11X + X2 = 24.25

Factor a perfect square on the left side:
(X + -5.5)(X + -5.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(X + -5.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
X + -5.5 = 4.924428901

Simplifying
X + -5.5 = 4.924428901

Reorder the terms:
-5.5 + X = 4.924428901

Solving
-5.5 + X = 4.924428901

Solving for variable 'X'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + X = 4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + X = 4.924428901 + 5.5
X = 4.924428901 + 5.5

Combine like terms: 4.924428901 + 5.5 = 10.424428901
X = 10.424428901

Simplifying
X = 10.424428901

Subproblem 2
X + -5.5 = -4.924428901

Simplifying
X + -5.5 = -4.924428901

Reorder the terms:
-5.5 + X = -4.924428901

Solving
-5.5 + X = -4.924428901

Solving for variable 'X'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + X = -4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + X = -4.924428901 + 5.5
X = -4.924428901 + 5.5

Combine like terms: -4.924428901 + 5.5 = 0.575571099
X = 0.575571099

Simplifying
X = 0.575571099

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {10.424428901, 0.575571099}