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

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

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

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

Reorder the terms:
4x + x2 + -7(2 + x) = 2(x + 2)(x + 4)
4x + x2 + (2 * -7 + x * -7) = 2(x + 2)(x + 4)
4x + x2 + (-14 + -7x) = 2(x + 2)(x + 4)

Reorder the terms:
-14 + 4x + -7x + x2 = 2(x + 2)(x + 4)

Combine like terms: 4x + -7x = -3x
-14 + -3x + x2 = 2(x + 2)(x + 4)

Reorder the terms:
-14 + -3x + x2 = 2(2 + x)(x + 4)

Reorder the terms:
-14 + -3x + x2 = 2(2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
-14 + -3x + x2 = 2(2(4 + x) + x(4 + x))
-14 + -3x + x2 = 2((4 * 2 + x * 2) + x(4 + x))
-14 + -3x + x2 = 2((8 + 2x) + x(4 + x))
-14 + -3x + x2 = 2(8 + 2x + (4 * x + x * x))
-14 + -3x + x2 = 2(8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
-14 + -3x + x2 = 2(8 + 6x + x2)
-14 + -3x + x2 = (8 * 2 + 6x * 2 + x2 * 2)
-14 + -3x + x2 = (16 + 12x + 2x2)

Solving
-14 + -3x + x2 = 16 + 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-14 + -16 + -3x + -12x + x2 + -2x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Combine like terms: -14 + -16 = -30
-30 + -3x + -12x + x2 + -2x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Combine like terms: -3x + -12x = -15x
-30 + -15x + x2 + -2x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-30 + -15x + -1x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Reorder the terms:
-30 + -15x + -1x2 = 16 + -16 + 12x + -12x + 2x2 + -2x2

Combine like terms: 16 + -16 = 0
-30 + -15x + -1x2 = 0 + 12x + -12x + 2x2 + -2x2
-30 + -15x + -1x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-30 + -15x + -1x2 = 0 + 2x2 + -2x2
-30 + -15x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + -15x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 15x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(30 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
30 + 15x + x2 = 0

Solving
30 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 15x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 15x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 15x + x2 = 0 + -30
15x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
15x + x2 = -30

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -30 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -30 + 56.25

Combine like terms: -30 + 56.25 = 26.25
56.25 + 15x + x2 = 26.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 7.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
x + 7.5 = 5.123475383

Simplifying
x + 7.5 = 5.123475383

Reorder the terms:
7.5 + x = 5.123475383

Solving
7.5 + x = 5.123475383

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 5.123475383 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 5.123475383 + -7.5
x = 5.123475383 + -7.5

Combine like terms: 5.123475383 + -7.5 = -2.376524617
x = -2.376524617

Simplifying
x = -2.376524617

Subproblem 2
x + 7.5 = -5.123475383

Simplifying
x + 7.5 = -5.123475383

Reorder the terms:
7.5 + x = -5.123475383

Solving
7.5 + x = -5.123475383

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -5.123475383 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -5.123475383 + -7.5
x = -5.123475383 + -7.5

Combine like terms: -5.123475383 + -7.5 = -12.623475383
x = -12.623475383

Simplifying
x = -12.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.376524617, -12.623475383}
Solution
x = {-2.376524617, -12.623475383}