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

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

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

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

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

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

Combine like terms: -1x + 1x = 0
3(-1 + 0 + x2) = (x + 2)(2x + -1)
3(-1 + x2) = (x + 2)(2x + -1)
(-1 * 3 + x2 * 3) = (x + 2)(2x + -1)
(-3 + 3x2) = (x + 2)(2x + -1)

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

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

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

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 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

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 = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638

Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

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 = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}