2(x-3)(x-2)=x+2-(x-4)

Solution for 2(x-3)(x-2)=x+2-(x-4) equation:

Simplifying
2(x + -3)(x + -2) = x + 2 + -1(x + -4)

Reorder the terms:
2(-3 + x)(x + -2) = x + 2 + -1(x + -4)

Reorder the terms:
2(-3 + x)(-2 + x) = x + 2 + -1(x + -4)

Multiply (-3 + x) * (-2 + x)
2(-3(-2 + x) + x(-2 + x)) = x + 2 + -1(x + -4)
2((-2 * -3 + x * -3) + x(-2 + x)) = x + 2 + -1(x + -4)
2((6 + -3x) + x(-2 + x)) = x + 2 + -1(x + -4)
2(6 + -3x + (-2 * x + x * x)) = x + 2 + -1(x + -4)
2(6 + -3x + (-2x + x2)) = x + 2 + -1(x + -4)

Combine like terms: -3x + -2x = -5x
2(6 + -5x + x2) = x + 2 + -1(x + -4)
(6 * 2 + -5x * 2 + x2 * 2) = x + 2 + -1(x + -4)
(12 + -10x + 2x2) = x + 2 + -1(x + -4)

Reorder the terms:
12 + -10x + 2x2 = x + 2 + -1(-4 + x)
12 + -10x + 2x2 = x + 2 + (-4 * -1 + x * -1)
12 + -10x + 2x2 = x + 2 + (4 + -1x)

Reorder the terms:
12 + -10x + 2x2 = 2 + 4 + x + -1x

Combine like terms: 2 + 4 = 6
12 + -10x + 2x2 = 6 + x + -1x

Combine like terms: x + -1x = 0
12 + -10x + 2x2 = 6 + 0
12 + -10x + 2x2 = 6

Solving
12 + -10x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
12 + -6 + -10x + 2x2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + -10x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -5x + x2 = 0

Solving
3 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -5x + x2 = 0 + -3

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

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

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5x + x2 = 3.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -2.5 = 1.802775638

Simplifying
x + -2.5 = 1.802775638

Reorder the terms:
-2.5 + x = 1.802775638

Solving
-2.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.802775638 + 2.5
x = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
x = 4.302775638

Simplifying
x = 4.302775638

Subproblem 2
x + -2.5 = -1.802775638

Simplifying
x + -2.5 = -1.802775638

Reorder the terms:
-2.5 + x = -1.802775638

Solving
-2.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.802775638 + 2.5
x = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
x = 0.697224362

Simplifying
x = 0.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.302775638, 0.697224362}
Solution
x = {4.302775638, 0.697224362}