(2x+5)(x-3)=(x+4)(x-1)

Solution for (2x+5)(x-3)=(x+4)(x-1) equation:

Simplifying
(2x + 5)(x + -3) = (x + 4)(x + -1)

Reorder the terms:
(5 + 2x)(x + -3) = (x + 4)(x + -1)

Reorder the terms:
(5 + 2x)(-3 + x) = (x + 4)(x + -1)

Multiply (5 + 2x) * (-3 + x)
(5(-3 + x) + 2x * (-3 + x)) = (x + 4)(x + -1)
((-3 * 5 + x * 5) + 2x * (-3 + x)) = (x + 4)(x + -1)
((-15 + 5x) + 2x * (-3 + x)) = (x + 4)(x + -1)
(-15 + 5x + (-3 * 2x + x * 2x)) = (x + 4)(x + -1)
(-15 + 5x + (-6x + 2x2)) = (x + 4)(x + -1)

Combine like terms: 5x + -6x = -1x
(-15 + -1x + 2x2) = (x + 4)(x + -1)

Reorder the terms:
-15 + -1x + 2x2 = (4 + x)(x + -1)

Reorder the terms:
-15 + -1x + 2x2 = (4 + x)(-1 + x)

Multiply (4 + x) * (-1 + x)
-15 + -1x + 2x2 = (4(-1 + x) + x(-1 + x))
-15 + -1x + 2x2 = ((-1 * 4 + x * 4) + x(-1 + x))
-15 + -1x + 2x2 = ((-4 + 4x) + x(-1 + x))
-15 + -1x + 2x2 = (-4 + 4x + (-1 * x + x * x))
-15 + -1x + 2x2 = (-4 + 4x + (-1x + x2))

Combine like terms: 4x + -1x = 3x
-15 + -1x + 2x2 = (-4 + 3x + x2)

Solving
-15 + -1x + 2x2 = -4 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-15 + 4 + -1x + -3x + 2x2 + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: -15 + 4 = -11
-11 + -1x + -3x + 2x2 + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: -1x + -3x = -4x
-11 + -4x + 2x2 + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-11 + -4x + 1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Reorder the terms:
-11 + -4x + 1x2 = -4 + 4 + 3x + -3x + x2 + -1x2

Combine like terms: -4 + 4 = 0
-11 + -4x + 1x2 = 0 + 3x + -3x + x2 + -1x2
-11 + -4x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-11 + -4x + 1x2 = 0 + x2 + -1x2
-11 + -4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + -4x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -4x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x + x2 = 0 + 11
-4x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4x + x2 = 11

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 11 + 4

Reorder the terms:
4 + -4x + x2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4x + x2 = 15

Factor a perfect square on the left side:
(x + -2)(x + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -2) equal to 3.872983346 and -3.872983346.

Subproblem 1
x + -2 = 3.872983346

Simplifying
x + -2 = 3.872983346

Reorder the terms:
-2 + x = 3.872983346

Solving
-2 + x = 3.872983346

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.872983346 + 2
x = 3.872983346 + 2

Combine like terms: 3.872983346 + 2 = 5.872983346
x = 5.872983346

Simplifying
x = 5.872983346

Subproblem 2
x + -2 = -3.872983346

Simplifying
x + -2 = -3.872983346

Reorder the terms:
-2 + x = -3.872983346

Solving
-2 + x = -3.872983346

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.872983346 + 2
x = -3.872983346 + 2

Combine like terms: -3.872983346 + 2 = -1.872983346
x = -1.872983346

Simplifying
x = -1.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.872983346, -1.872983346}