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

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

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

Reorder the terms:
3(2 + 3x) = (x + -1)(x + 1)
(2 * 3 + 3x * 3) = (x + -1)(x + 1)
(6 + 9x) = (x + -1)(x + 1)

Reorder the terms:
6 + 9x = (-1 + x)(x + 1)

Reorder the terms:
6 + 9x = (-1 + x)(1 + x)

Multiply (-1 + x) * (1 + x)
6 + 9x = (-1(1 + x) + x(1 + x))
6 + 9x = ((1 * -1 + x * -1) + x(1 + x))
6 + 9x = ((-1 + -1x) + x(1 + x))
6 + 9x = (-1 + -1x + (1 * x + x * x))
6 + 9x = (-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
6 + 9x = (-1 + 0 + x2)
6 + 9x = (-1 + x2)

Solving
6 + 9x = -1 + x2

Solving for variable 'x'.

Reorder the terms:
6 + 1 + 9x + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: 6 + 1 = 7
7 + 9x + -1x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
7 + 9x + -1x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
7 + 9x + -1x2 = 0 + x2 + -1x2
7 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 9x + -1x2 = 0

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

Divide each side by '-1'.
-7 + -9x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -9x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -9x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -9x + x2 = 0 + 7
-9x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-9x + x2 = 7

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 7 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 7 + 20.25

Combine like terms: 7 + 20.25 = 27.25
20.25 + -9x + x2 = 27.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + -4.5 = 5.220153254

Simplifying
x + -4.5 = 5.220153254

Reorder the terms:
-4.5 + x = 5.220153254

Solving
-4.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 5.220153254 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.220153254 + 4.5
x = 5.220153254 + 4.5

Combine like terms: 5.220153254 + 4.5 = 9.720153254
x = 9.720153254

Simplifying
x = 9.720153254

Subproblem 2
x + -4.5 = -5.220153254

Simplifying
x + -4.5 = -5.220153254

Reorder the terms:
-4.5 + x = -5.220153254

Solving
-4.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -5.220153254 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.220153254 + 4.5
x = -5.220153254 + 4.5

Combine like terms: -5.220153254 + 4.5 = -0.720153254
x = -0.720153254

Simplifying
x = -0.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.720153254, -0.720153254}