2(x-3)x-3(x-1)=5(x-2)-3

Solution for 2(x-3)x-3(x-1)=5(x-2)-3 equation:

Simplifying
2(x + -3) * x + -3(x + -1) = 5(x + -2) + -3

Reorder the terms:
2(-3 + x) * x + -3(x + -1) = 5(x + -2) + -3

Reorder the terms for easier multiplication:
2x(-3 + x) + -3(x + -1) = 5(x + -2) + -3
(-3 * 2x + x * 2x) + -3(x + -1) = 5(x + -2) + -3
(-6x + 2x2) + -3(x + -1) = 5(x + -2) + -3

Reorder the terms:
-6x + 2x2 + -3(-1 + x) = 5(x + -2) + -3
-6x + 2x2 + (-1 * -3 + x * -3) = 5(x + -2) + -3
-6x + 2x2 + (3 + -3x) = 5(x + -2) + -3

Reorder the terms:
3 + -6x + -3x + 2x2 = 5(x + -2) + -3

Combine like terms: -6x + -3x = -9x
3 + -9x + 2x2 = 5(x + -2) + -3

Reorder the terms:
3 + -9x + 2x2 = 5(-2 + x) + -3
3 + -9x + 2x2 = (-2 * 5 + x * 5) + -3
3 + -9x + 2x2 = (-10 + 5x) + -3

Reorder the terms:
3 + -9x + 2x2 = -10 + -3 + 5x

Combine like terms: -10 + -3 = -13
3 + -9x + 2x2 = -13 + 5x

Solving
3 + -9x + 2x2 = -13 + 5x

Solving for variable 'x'.

Reorder the terms:
3 + 13 + -9x + -5x + 2x2 = -13 + 5x + 13 + -5x

Combine like terms: 3 + 13 = 16
16 + -9x + -5x + 2x2 = -13 + 5x + 13 + -5x

Combine like terms: -9x + -5x = -14x
16 + -14x + 2x2 = -13 + 5x + 13 + -5x

Reorder the terms:
16 + -14x + 2x2 = -13 + 13 + 5x + -5x

Combine like terms: -13 + 13 = 0
16 + -14x + 2x2 = 0 + 5x + -5x
16 + -14x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
16 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -7x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -7x + x2 = 0

Solving
8 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -7x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x + x2 = 0 + -8
-7x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7x + x2 = -8

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -8 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7x + x2 = 4.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + -3.5 = 2.061552813

Simplifying
x + -3.5 = 2.061552813

Reorder the terms:
-3.5 + x = 2.061552813

Solving
-3.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.061552813 + 3.5
x = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
x = 5.561552813

Simplifying
x = 5.561552813

Subproblem 2
x + -3.5 = -2.061552813

Simplifying
x + -3.5 = -2.061552813

Reorder the terms:
-3.5 + x = -2.061552813

Solving
-3.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.061552813 + 3.5
x = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
x = 1.438447187

Simplifying
x = 1.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.561552813, 1.438447187}
Solution
x = {5.561552813, 1.438447187}