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

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

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

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

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

Multiply (-6 + 3x) * (2 + x)
(-6(2 + x) + 3x * (2 + x)) = (x + -1)(x + 3)
((2 * -6 + x * -6) + 3x * (2 + x)) = (x + -1)(x + 3)
((-12 + -6x) + 3x * (2 + x)) = (x + -1)(x + 3)
(-12 + -6x + (2 * 3x + x * 3x)) = (x + -1)(x + 3)
(-12 + -6x + (6x + 3x2)) = (x + -1)(x + 3)

Combine like terms: -6x + 6x = 0
(-12 + 0 + 3x2) = (x + -1)(x + 3)
(-12 + 3x2) = (x + -1)(x + 3)

Reorder the terms:
-12 + 3x2 = (-1 + x)(x + 3)

Reorder the terms:
-12 + 3x2 = (-1 + x)(3 + x)

Multiply (-1 + x) * (3 + x)
-12 + 3x2 = (-1(3 + x) + x(3 + x))
-12 + 3x2 = ((3 * -1 + x * -1) + x(3 + x))
-12 + 3x2 = ((-3 + -1x) + x(3 + x))
-12 + 3x2 = (-3 + -1x + (3 * x + x * x))
-12 + 3x2 = (-3 + -1x + (3x + x2))

Combine like terms: -1x + 3x = 2x
-12 + 3x2 = (-3 + 2x + x2)

Solving
-12 + 3x2 = -3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + 3 + -2x + 3x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -12 + 3 = -9
-9 + -2x + 3x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

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

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

Combine like terms: -3 + 3 = 0
-9 + -2x + 2x2 = 0 + 2x + -2x + x2 + -1x2
-9 + -2x + 2x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-9 + -2x + 2x2 = 0 + x2 + -1x2
-9 + -2x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + -2x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -1x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1x + x2 = 0 + 4.5
-1x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1x + x2 = 4.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4.5 + 0.25

Combine like terms: 4.5 + 0.25 = 4.75
0.25 + -1x + x2 = 4.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.179449472 and -2.179449472.

Subproblem 1
x + -0.5 = 2.179449472

Simplifying
x + -0.5 = 2.179449472

Reorder the terms:
-0.5 + x = 2.179449472

Solving
-0.5 + x = 2.179449472

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.179449472 + 0.5
x = 2.179449472 + 0.5

Combine like terms: 2.179449472 + 0.5 = 2.679449472
x = 2.679449472

Simplifying
x = 2.679449472

Subproblem 2
x + -0.5 = -2.179449472

Simplifying
x + -0.5 = -2.179449472

Reorder the terms:
-0.5 + x = -2.179449472

Solving
-0.5 + x = -2.179449472

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.179449472 + 0.5
x = -2.179449472 + 0.5

Combine like terms: -2.179449472 + 0.5 = -1.679449472
x = -1.679449472

Simplifying
x = -1.679449472

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.679449472, -1.679449472}