4*9=(x+2)(x-2+x+4)

Solution for 4*9=(x+2)(x-2+x+4) equation:

Simplifying
4 * 9 = (x + 2)(x + -2 + x + 4)

Multiply 4 * 9
36 = (x + 2)(x + -2 + x + 4)

Reorder the terms:
36 = (2 + x)(x + -2 + x + 4)

Reorder the terms:
36 = (2 + x)(-2 + 4 + x + x)

Combine like terms: -2 + 4 = 2
36 = (2 + x)(2 + x + x)

Combine like terms: x + x = 2x
36 = (2 + x)(2 + 2x)

Multiply (2 + x) * (2 + 2x)
36 = (2(2 + 2x) + x(2 + 2x))
36 = ((2 * 2 + 2x * 2) + x(2 + 2x))
36 = ((4 + 4x) + x(2 + 2x))
36 = (4 + 4x + (2 * x + 2x * x))
36 = (4 + 4x + (2x + 2x2))

Combine like terms: 4x + 2x = 6x
36 = (4 + 6x + 2x2)

Solving
36 = 4 + 6x + 2x2

Solving for variable 'x'.

Combine like terms: 36 + -4 = 32
32 + -6x + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2

Reorder the terms:
32 + -6x + -2x2 = 4 + -4 + 6x + -6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
32 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2
32 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
32 + -6x + -2x2 = 0 + 2x2 + -2x2
32 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -3x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -3x + -1x2)' equal to zero and attempt to solve:

Simplifying
16 + -3x + -1x2 = 0

Solving
16 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 3x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 3x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3x + x2 = 0 + 16
3x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
3x + x2 = 16

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 16 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3x + x2 = 18.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + 1.5 = 4.272001873

Simplifying
x + 1.5 = 4.272001873

Reorder the terms:
1.5 + x = 4.272001873

Solving
1.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.272001873 + -1.5
x = 4.272001873 + -1.5

Combine like terms: 4.272001873 + -1.5 = 2.772001873
x = 2.772001873

Simplifying
x = 2.772001873

Subproblem 2
x + 1.5 = -4.272001873

Simplifying
x + 1.5 = -4.272001873

Reorder the terms:
1.5 + x = -4.272001873

Solving
1.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.272001873 + -1.5
x = -4.272001873 + -1.5

Combine like terms: -4.272001873 + -1.5 = -5.772001873
x = -5.772001873

Simplifying
x = -5.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.772001873, -5.772001873}
Solution
x = {2.772001873, -5.772001873}