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

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

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

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

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

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

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

Reorder the terms for easier multiplication:
-6 + 1x + x2 = 2x + 1

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

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: 1 + -1 = 0
-7 + -1x + x2 = 0 + 2x + -2x
-7 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-7 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -1x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -1x + x2 = 0 + 7

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

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

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 = 7 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + -1x + x2 = 7.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
x + -0.5 = 2.692582404

Simplifying
x + -0.5 = 2.692582404

Reorder the terms:
-0.5 + x = 2.692582404

Solving
-0.5 + x = 2.692582404

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 = 2.692582404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.692582404 + 0.5
x = 2.692582404 + 0.5

Combine like terms: 2.692582404 + 0.5 = 3.192582404
x = 3.192582404

Simplifying
x = 3.192582404

Subproblem 2
x + -0.5 = -2.692582404

Simplifying
x + -0.5 = -2.692582404

Reorder the terms:
-0.5 + x = -2.692582404

Solving
-0.5 + x = -2.692582404

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 = -2.692582404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.692582404 + 0.5
x = -2.692582404 + 0.5

Combine like terms: -2.692582404 + 0.5 = -2.192582404
x = -2.192582404

Simplifying
x = -2.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.192582404, -2.192582404}