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

Solution for (x+3)(x+2)=(2x-4)(x+1) equation:

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

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

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

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

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

Reorder the terms:
6 + 5x + x2 = (-4 + 2x)(x + 1)

Reorder the terms:
6 + 5x + x2 = (-4 + 2x)(1 + x)

Multiply (-4 + 2x) * (1 + x)
6 + 5x + x2 = (-4(1 + x) + 2x * (1 + x))
6 + 5x + x2 = ((1 * -4 + x * -4) + 2x * (1 + x))
6 + 5x + x2 = ((-4 + -4x) + 2x * (1 + x))
6 + 5x + x2 = (-4 + -4x + (1 * 2x + x * 2x))
6 + 5x + x2 = (-4 + -4x + (2x + 2x2))

Combine like terms: -4x + 2x = -2x
6 + 5x + x2 = (-4 + -2x + 2x2)

Solving
6 + 5x + x2 = -4 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + 4 + 5x + 2x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2

Combine like terms: 6 + 4 = 10
10 + 5x + 2x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2

Combine like terms: 5x + 2x = 7x
10 + 7x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2

Combine like terms: x2 + -2x2 = -1x2
10 + 7x + -1x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2

Reorder the terms:
10 + 7x + -1x2 = -4 + 4 + -2x + 2x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
10 + 7x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2
10 + 7x + -1x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
10 + 7x + -1x2 = 0 + 2x2 + -2x2
10 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-10 + -7x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -7x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -7x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7x + x2 = 0 + 10
-7x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-7x + x2 = 10

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 = 10 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + -7x + x2 = 22.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + -3.5 = 4.716990566

Simplifying
x + -3.5 = 4.716990566

Reorder the terms:
-3.5 + x = 4.716990566

Solving
-3.5 + x = 4.716990566

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 = 4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.716990566 + 3.5
x = 4.716990566 + 3.5

Combine like terms: 4.716990566 + 3.5 = 8.216990566
x = 8.216990566

Simplifying
x = 8.216990566

Subproblem 2
x + -3.5 = -4.716990566

Simplifying
x + -3.5 = -4.716990566

Reorder the terms:
-3.5 + x = -4.716990566

Solving
-3.5 + x = -4.716990566

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 = -4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.716990566 + 3.5
x = -4.716990566 + 3.5

Combine like terms: -4.716990566 + 3.5 = -1.216990566
x = -1.216990566

Simplifying
x = -1.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.216990566, -1.216990566}