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

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

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

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

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

Multiply (-1 + 3x) * (3 + 2x)
(-1(3 + 2x) + 3x * (3 + 2x)) = x(x) + 2(x + -1)
((3 * -1 + 2x * -1) + 3x * (3 + 2x)) = x(x) + 2(x + -1)
((-3 + -2x) + 3x * (3 + 2x)) = x(x) + 2(x + -1)
(-3 + -2x + (3 * 3x + 2x * 3x)) = x(x) + 2(x + -1)
(-3 + -2x + (9x + 6x2)) = x(x) + 2(x + -1)

Combine like terms: -2x + 9x = 7x
(-3 + 7x + 6x2) = x(x) + 2(x + -1)

Multiply x * x
-3 + 7x + 6x2 = x2 + 2(x + -1)

Reorder the terms:
-3 + 7x + 6x2 = x2 + 2(-1 + x)
-3 + 7x + 6x2 = x2 + (-1 * 2 + x * 2)
-3 + 7x + 6x2 = x2 + (-2 + 2x)

Reorder the terms:
-3 + 7x + 6x2 = -2 + 2x + x2

Solving
-3 + 7x + 6x2 = -2 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 2 + 7x + -2x + 6x2 + -1x2 = -2 + 2x + x2 + 2 + -2x + -1x2

Combine like terms: -3 + 2 = -1
-1 + 7x + -2x + 6x2 + -1x2 = -2 + 2x + x2 + 2 + -2x + -1x2

Combine like terms: 7x + -2x = 5x
-1 + 5x + 6x2 + -1x2 = -2 + 2x + x2 + 2 + -2x + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
-1 + 5x + 5x2 = -2 + 2x + x2 + 2 + -2x + -1x2

Reorder the terms:
-1 + 5x + 5x2 = -2 + 2 + 2x + -2x + x2 + -1x2

Combine like terms: -2 + 2 = 0
-1 + 5x + 5x2 = 0 + 2x + -2x + x2 + -1x2
-1 + 5x + 5x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-1 + 5x + 5x2 = 0 + x2 + -1x2
-1 + 5x + 5x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + 5x + 5x2 = 0

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

Divide each side by '5'.
-0.2 + x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x + x2 = 0 + 0.2
x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
x + x2 = 0.2

The x term is x.  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.
 + 0.25 + x2 = 0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
1.25 + x2 = 0.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
x + 0.5 = 0.670820393

Simplifying
x + 0.5 = 0.670820393

Reorder the terms:
0.5 + x = 0.670820393

Solving
0.5 + x = 0.670820393

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 = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.670820393 + -0.5
x = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
x = 0.170820393

Simplifying
x = 0.170820393

Subproblem 2
x + 0.5 = -0.670820393

Simplifying
x + 0.5 = -0.670820393

Reorder the terms:
0.5 + x = -0.670820393

Solving
0.5 + x = -0.670820393

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 = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.670820393 + -0.5
x = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
x = -1.170820393

Simplifying
x = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.170820393, -1.170820393}