(2x+39)(x-1)=(x+2)(x-1)+2

Solution for (2x+39)(x-1)=(x+2)(x-1)+2 equation:

Simplifying
(2x + 39)(x + -1) = (x + 2)(x + -1) + 2

Reorder the terms:
(39 + 2x)(x + -1) = (x + 2)(x + -1) + 2

Reorder the terms:
(39 + 2x)(-1 + x) = (x + 2)(x + -1) + 2

Multiply (39 + 2x) * (-1 + x)
(39(-1 + x) + 2x * (-1 + x)) = (x + 2)(x + -1) + 2
((-1 * 39 + x * 39) + 2x * (-1 + x)) = (x + 2)(x + -1) + 2
((-39 + 39x) + 2x * (-1 + x)) = (x + 2)(x + -1) + 2
(-39 + 39x + (-1 * 2x + x * 2x)) = (x + 2)(x + -1) + 2
(-39 + 39x + (-2x + 2x2)) = (x + 2)(x + -1) + 2

Combine like terms: 39x + -2x = 37x
(-39 + 37x + 2x2) = (x + 2)(x + -1) + 2

Reorder the terms:
-39 + 37x + 2x2 = (2 + x)(x + -1) + 2

Reorder the terms:
-39 + 37x + 2x2 = (2 + x)(-1 + x) + 2

Multiply (2 + x) * (-1 + x)
-39 + 37x + 2x2 = (2(-1 + x) + x(-1 + x)) + 2
-39 + 37x + 2x2 = ((-1 * 2 + x * 2) + x(-1 + x)) + 2
-39 + 37x + 2x2 = ((-2 + 2x) + x(-1 + x)) + 2
-39 + 37x + 2x2 = (-2 + 2x + (-1 * x + x * x)) + 2
-39 + 37x + 2x2 = (-2 + 2x + (-1x + x2)) + 2

Combine like terms: 2x + -1x = 1x
-39 + 37x + 2x2 = (-2 + 1x + x2) + 2

Reorder the terms:
-39 + 37x + 2x2 = -2 + 2 + 1x + x2

Combine like terms: -2 + 2 = 0
-39 + 37x + 2x2 = 0 + 1x + x2
-39 + 37x + 2x2 = 1x + x2

Solving
-39 + 37x + 2x2 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
-39 + 37x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 37x + -1x = 36x
-39 + 36x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-39 + 36x + 1x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-39 + 36x + 1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-39 + 36x + 1x2 = 0 + x2 + -1x2
-39 + 36x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-39 + 36x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 36x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + 36x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 36x + x2 = 0 + 39
36x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
36x + x2 = 39

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 39 + 324

Reorder the terms:
324 + 36x + x2 = 39 + 324

Combine like terms: 39 + 324 = 363
324 + 36x + x2 = 363

Factor a perfect square on the left side:
(x + 18)(x + 18) = 363

Calculate the square root of the right side: 19.052558883

Break this problem into two subproblems by setting 
(x + 18) equal to 19.052558883 and -19.052558883.

Subproblem 1
x + 18 = 19.052558883

Simplifying
x + 18 = 19.052558883

Reorder the terms:
18 + x = 19.052558883

Solving
18 + x = 19.052558883

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 19.052558883 + -18

Combine like terms: 18 + -18 = 0
0 + x = 19.052558883 + -18
x = 19.052558883 + -18

Combine like terms: 19.052558883 + -18 = 1.052558883
x = 1.052558883

Simplifying
x = 1.052558883

Subproblem 2
x + 18 = -19.052558883

Simplifying
x + 18 = -19.052558883

Reorder the terms:
18 + x = -19.052558883

Solving
18 + x = -19.052558883

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -19.052558883 + -18

Combine like terms: 18 + -18 = 0
0 + x = -19.052558883 + -18
x = -19.052558883 + -18

Combine like terms: -19.052558883 + -18 = -37.052558883
x = -37.052558883

Simplifying
x = -37.052558883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.052558883, -37.052558883}