9=(4+2x)(6+2x)-24

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Solution for 9=(4+2x)(6+2x)-24 equation: 


Simplifying
9 = (4 + 2x)(6 + 2x) + -24

Multiply (4 + 2x) * (6 + 2x)
9 = (4(6 + 2x) + 2x * (6 + 2x)) + -24
9 = ((6 * 4 + 2x * 4) + 2x * (6 + 2x)) + -24
9 = ((24 + 8x) + 2x * (6 + 2x)) + -24
9 = (24 + 8x + (6 * 2x + 2x * 2x)) + -24
9 = (24 + 8x + (12x + 4x2)) + -24

Combine like terms: 8x + 12x = 20x
9 = (24 + 20x + 4x2) + -24

Reorder the terms:
9 = 24 + -24 + 20x + 4x2

Combine like terms: 24 + -24 = 0
9 = 0 + 20x + 4x2
9 = 20x + 4x2

Solving
9 = 20x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -20x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
9 + -20x + -4x2 = 0 + 4x2 + -4x2
9 + -20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + -20x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + 5x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 5x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 5x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 5x + x2 = 0 + 2.25
5x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
5x + x2 = 2.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.25 + 6.25

Combine like terms: 2.25 + 6.25 = 8.5
6.25 + 5x + x2 = 8.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.915475947 and -2.915475947.


Subproblem 1
x + 2.5 = 2.915475947

Simplifying
x + 2.5 = 2.915475947

Reorder the terms:
2.5 + x = 2.915475947

Solving
2.5 + x = 2.915475947

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.915475947 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.915475947 + -2.5
x = 2.915475947 + -2.5

Combine like terms: 2.915475947 + -2.5 = 0.415475947
x = 0.415475947

Simplifying
x = 0.415475947


Subproblem 2
x + 2.5 = -2.915475947

Simplifying
x + 2.5 = -2.915475947

Reorder the terms:
2.5 + x = -2.915475947

Solving
2.5 + x = -2.915475947

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.915475947 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.915475947 + -2.5
x = -2.915475947 + -2.5

Combine like terms: -2.915475947 + -2.5 = -5.415475947
x = -5.415475947

Simplifying
x = -5.415475947


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.415475947, -5.415475947}

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