(x-4)-6(x+1)=(x+1)(x+4)

Solution for (x-4)-6(x+1)=(x+1)(x+4) equation:

Simplifying
(x + -4) + -6(x + 1) = (x + 1)(x + 4)

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

Remove parenthesis around (-4 + x)
-4 + x + -6(x + 1) = (x + 1)(x + 4)

Reorder the terms:
-4 + x + -6(1 + x) = (x + 1)(x + 4)
-4 + x + (1 * -6 + x * -6) = (x + 1)(x + 4)
-4 + x + (-6 + -6x) = (x + 1)(x + 4)

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

Combine like terms: -4 + -6 = -10
-10 + x + -6x = (x + 1)(x + 4)

Combine like terms: x + -6x = -5x
-10 + -5x = (x + 1)(x + 4)

Reorder the terms:
-10 + -5x = (1 + x)(x + 4)

Reorder the terms:
-10 + -5x = (1 + x)(4 + x)

Multiply (1 + x) * (4 + x)
-10 + -5x = (1(4 + x) + x(4 + x))
-10 + -5x = ((4 * 1 + x * 1) + x(4 + x))
-10 + -5x = ((4 + 1x) + x(4 + x))
-10 + -5x = (4 + 1x + (4 * x + x * x))
-10 + -5x = (4 + 1x + (4x + x2))

Combine like terms: 1x + 4x = 5x
-10 + -5x = (4 + 5x + x2)

Solving
-10 + -5x = 4 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + -4 + -5x + -5x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Combine like terms: -10 + -4 = -14
-14 + -5x + -5x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Combine like terms: -5x + -5x = -10x
-14 + -10x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Reorder the terms:
-14 + -10x + -1x2 = 4 + -4 + 5x + -5x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-14 + -10x + -1x2 = 0 + 5x + -5x + x2 + -1x2
-14 + -10x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-14 + -10x + -1x2 = 0 + x2 + -1x2
-14 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + -10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 10x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(14 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
14 + 10x + x2 = 0

Solving
14 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 10x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 10x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 10x + x2 = 0 + -14
10x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
10x + x2 = -14

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -14 + 25

Reorder the terms:
25 + 10x + x2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + 10x + x2 = 11

Factor a perfect square on the left side:
(x + 5)(x + 5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 5) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + 5 = 3.31662479

Simplifying
x + 5 = 3.31662479

Reorder the terms:
5 + x = 3.31662479

Solving
5 + x = 3.31662479

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.31662479 + -5
x = 3.31662479 + -5

Combine like terms: 3.31662479 + -5 = -1.68337521
x = -1.68337521

Simplifying
x = -1.68337521

Subproblem 2
x + 5 = -3.31662479

Simplifying
x + 5 = -3.31662479

Reorder the terms:
5 + x = -3.31662479

Solving
5 + x = -3.31662479

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.31662479 + -5
x = -3.31662479 + -5

Combine like terms: -3.31662479 + -5 = -8.31662479
x = -8.31662479

Simplifying
x = -8.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.68337521, -8.31662479}
Solution
x = {-1.68337521, -8.31662479}