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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

Reorder the terms:
-9 + -2x + 1x2 = 3 + -3 + 1x + -1x + x2 + -1x2

Combine like terms: 3 + -3 = 0
-9 + -2x + 1x2 = 0 + 1x + -1x + x2 + -1x2
-9 + -2x + 1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-9 + -2x + 1x2 = 0 + x2 + -1x2
-9 + -2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + -2x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x + x2 = 0 + 9
-2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2x + x2 = 9

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + -2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2x + x2 = 10

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -1 = 3.16227766

Simplifying
x + -1 = 3.16227766

Reorder the terms:
-1 + x = 3.16227766

Solving
-1 + x = 3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.16227766 + 1
x = 3.16227766 + 1

Combine like terms: 3.16227766 + 1 = 4.16227766
x = 4.16227766

Simplifying
x = 4.16227766

Subproblem 2
x + -1 = -3.16227766

Simplifying
x + -1 = -3.16227766

Reorder the terms:
-1 + x = -3.16227766

Solving
-1 + x = -3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.16227766 + 1
x = -3.16227766 + 1

Combine like terms: -3.16227766 + 1 = -2.16227766
x = -2.16227766

Simplifying
x = -2.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.16227766, -2.16227766}