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

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

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

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

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

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

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

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

Solving
6 + 3x = -1 + x2

Solving for variable 'x'.

Reorder the terms:
6 + 1 + 3x + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: 6 + 1 = 7
7 + 3x + -1x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
7 + 3x + -1x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
7 + 3x + -1x2 = 0 + x2 + -1x2
7 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-7 + -3x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x + x2 = 0 + 7
-3x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3x + x2 = 7

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 7 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3x + x2 = 9.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
x + -1.5 = 3.041381265

Simplifying
x + -1.5 = 3.041381265

Reorder the terms:
-1.5 + x = 3.041381265

Solving
-1.5 + x = 3.041381265

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.041381265 + 1.5
x = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
x = 4.541381265

Simplifying
x = 4.541381265

Subproblem 2
x + -1.5 = -3.041381265

Simplifying
x + -1.5 = -3.041381265

Reorder the terms:
-1.5 + x = -3.041381265

Solving
-1.5 + x = -3.041381265

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.041381265 + 1.5
x = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
x = -1.541381265

Simplifying
x = -1.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.541381265, -1.541381265}