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

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

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

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

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

Multiply (3 + 2x) * (-2 + x)
(3(-2 + x) + 2x * (-2 + x)) = x(x + -1) + (x + 3)
((-2 * 3 + x * 3) + 2x * (-2 + x)) = x(x + -1) + (x + 3)
((-6 + 3x) + 2x * (-2 + x)) = x(x + -1) + (x + 3)
(-6 + 3x + (-2 * 2x + x * 2x)) = x(x + -1) + (x + 3)
(-6 + 3x + (-4x + 2x2)) = x(x + -1) + (x + 3)

Combine like terms: 3x + -4x = -1x
(-6 + -1x + 2x2) = x(x + -1) + (x + 3)

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

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

Remove parenthesis around (3 + x)
-6 + -1x + 2x2 = -1x + x2 + 3 + x

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

Combine like terms: -1x + x = 0
-6 + -1x + 2x2 = 3 + 0 + x2
-6 + -1x + 2x2 = 3 + x2

Solving
-6 + -1x + 2x2 = 3 + x2

Solving for variable 'x'.

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

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -1x + x2 = 0 + 9

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

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

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 = 9 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + -1x + x2 = 9.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
x + -0.5 = 3.041381265

Simplifying
x + -0.5 = 3.041381265

Reorder the terms:
-0.5 + x = 3.041381265

Solving
-0.5 + x = 3.041381265

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 = 3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.041381265 + 0.5
x = 3.041381265 + 0.5

Combine like terms: 3.041381265 + 0.5 = 3.541381265
x = 3.541381265

Simplifying
x = 3.541381265

Subproblem 2
x + -0.5 = -3.041381265

Simplifying
x + -0.5 = -3.041381265

Reorder the terms:
-0.5 + x = -3.041381265

Solving
-0.5 + x = -3.041381265

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 = -3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.041381265 + 0.5
x = -3.041381265 + 0.5

Combine like terms: -3.041381265 + 0.5 = -2.541381265
x = -2.541381265

Simplifying
x = -2.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.541381265, -2.541381265}