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

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

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

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

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

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

Combine like terms: -3x + -6x = -9x
(9 + -9x + 2x2) = (3x + 1)(6 + -1x)

Reorder the terms:
9 + -9x + 2x2 = (1 + 3x)(6 + -1x)

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

Combine like terms: -1x + 18x = 17x
9 + -9x + 2x2 = (6 + 17x + -3x2)

Solving
9 + -9x + 2x2 = 6 + 17x + -3x2

Solving for variable 'x'.

Reorder the terms:
9 + -6 + -9x + -17x + 2x2 + 3x2 = 6 + 17x + -3x2 + -6 + -17x + 3x2

Combine like terms: 9 + -6 = 3
3 + -9x + -17x + 2x2 + 3x2 = 6 + 17x + -3x2 + -6 + -17x + 3x2

Combine like terms: -9x + -17x = -26x
3 + -26x + 2x2 + 3x2 = 6 + 17x + -3x2 + -6 + -17x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
3 + -26x + 5x2 = 6 + 17x + -3x2 + -6 + -17x + 3x2

Reorder the terms:
3 + -26x + 5x2 = 6 + -6 + 17x + -17x + -3x2 + 3x2

Combine like terms: 6 + -6 = 0
3 + -26x + 5x2 = 0 + 17x + -17x + -3x2 + 3x2
3 + -26x + 5x2 = 17x + -17x + -3x2 + 3x2

Combine like terms: 17x + -17x = 0
3 + -26x + 5x2 = 0 + -3x2 + 3x2
3 + -26x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
3 + -26x + 5x2 = 0

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

Divide each side by '5'.
0.6 + -5.2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -5.2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -5.2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -5.2x + x2 = 0 + -0.6
-5.2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-5.2x + x2 = -0.6

The x term is -5.2x.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2x + 6.76 + x2 = -0.6 + 6.76

Reorder the terms:
6.76 + -5.2x + x2 = -0.6 + 6.76

Combine like terms: -0.6 + 6.76 = 6.16
6.76 + -5.2x + x2 = 6.16

Factor a perfect square on the left side:
(x + -2.6)(x + -2.6) = 6.16

Calculate the square root of the right side: 2.481934729

Break this problem into two subproblems by setting 
(x + -2.6) equal to 2.481934729 and -2.481934729.

Subproblem 1
x + -2.6 = 2.481934729

Simplifying
x + -2.6 = 2.481934729

Reorder the terms:
-2.6 + x = 2.481934729

Solving
-2.6 + x = 2.481934729

Solving for variable 'x'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + x = 2.481934729 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + x = 2.481934729 + 2.6
x = 2.481934729 + 2.6

Combine like terms: 2.481934729 + 2.6 = 5.081934729
x = 5.081934729

Simplifying
x = 5.081934729

Subproblem 2
x + -2.6 = -2.481934729

Simplifying
x + -2.6 = -2.481934729

Reorder the terms:
-2.6 + x = -2.481934729

Solving
-2.6 + x = -2.481934729

Solving for variable 'x'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + x = -2.481934729 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + x = -2.481934729 + 2.6
x = -2.481934729 + 2.6

Combine like terms: -2.481934729 + 2.6 = 0.118065271
x = 0.118065271

Simplifying
x = 0.118065271

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.081934729, 0.118065271}