(x+7)(x-1)=(2x+1)(x-4)

Solution for (x+7)(x-1)=(2x+1)(x-4) equation:

Simplifying
(x + 7)(x + -1) = (2x + 1)(x + -4)

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

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

Multiply (7 + x) * (-1 + x)
(7(-1 + x) + x(-1 + x)) = (2x + 1)(x + -4)
((-1 * 7 + x * 7) + x(-1 + x)) = (2x + 1)(x + -4)
((-7 + 7x) + x(-1 + x)) = (2x + 1)(x + -4)
(-7 + 7x + (-1 * x + x * x)) = (2x + 1)(x + -4)
(-7 + 7x + (-1x + x2)) = (2x + 1)(x + -4)

Combine like terms: 7x + -1x = 6x
(-7 + 6x + x2) = (2x + 1)(x + -4)

Reorder the terms:
-7 + 6x + x2 = (1 + 2x)(x + -4)

Reorder the terms:
-7 + 6x + x2 = (1 + 2x)(-4 + x)

Multiply (1 + 2x) * (-4 + x)
-7 + 6x + x2 = (1(-4 + x) + 2x * (-4 + x))
-7 + 6x + x2 = ((-4 * 1 + x * 1) + 2x * (-4 + x))
-7 + 6x + x2 = ((-4 + 1x) + 2x * (-4 + x))
-7 + 6x + x2 = (-4 + 1x + (-4 * 2x + x * 2x))
-7 + 6x + x2 = (-4 + 1x + (-8x + 2x2))

Combine like terms: 1x + -8x = -7x
-7 + 6x + x2 = (-4 + -7x + 2x2)

Solving
-7 + 6x + x2 = -4 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 4 + 6x + 7x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: -7 + 4 = -3
-3 + 6x + 7x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: 6x + 7x = 13x
-3 + 13x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-3 + 13x + -1x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Reorder the terms:
-3 + 13x + -1x2 = -4 + 4 + -7x + 7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
-3 + 13x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2
-3 + 13x + -1x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-3 + 13x + -1x2 = 0 + 2x2 + -2x2
-3 + 13x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -13x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -13x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -13x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -13x + x2 = 0 + -3
-13x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-13x + x2 = -3

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -3 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -3 + 42.25

Combine like terms: -3 + 42.25 = 39.25
42.25 + -13x + x2 = 39.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.264982043 and -6.264982043.

Subproblem 1
x + -6.5 = 6.264982043

Simplifying
x + -6.5 = 6.264982043

Reorder the terms:
-6.5 + x = 6.264982043

Solving
-6.5 + x = 6.264982043

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 6.264982043 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.264982043 + 6.5
x = 6.264982043 + 6.5

Combine like terms: 6.264982043 + 6.5 = 12.764982043
x = 12.764982043

Simplifying
x = 12.764982043

Subproblem 2
x + -6.5 = -6.264982043

Simplifying
x + -6.5 = -6.264982043

Reorder the terms:
-6.5 + x = -6.264982043

Solving
-6.5 + x = -6.264982043

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -6.264982043 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.264982043 + 6.5
x = -6.264982043 + 6.5

Combine like terms: -6.264982043 + 6.5 = 0.235017957
x = 0.235017957

Simplifying
x = 0.235017957

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.764982043, 0.235017957}