(12+2x)(8+2x)=288

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Solution for (12+2x)(8+2x)=288 equation: 


Simplifying
(12 + 2x)(8 + 2x) = 288

Multiply (12 + 2x) * (8 + 2x)
(12(8 + 2x) + 2x * (8 + 2x)) = 288
((8 * 12 + 2x * 12) + 2x * (8 + 2x)) = 288
((96 + 24x) + 2x * (8 + 2x)) = 288
(96 + 24x + (8 * 2x + 2x * 2x)) = 288
(96 + 24x + (16x + 4x2)) = 288

Combine like terms: 24x + 16x = 40x
(96 + 40x + 4x2) = 288

Solving
96 + 40x + 4x2 = 288

Solving for variable 'x'.

Reorder the terms:
96 + -288 + 40x + 4x2 = 288 + -288

Combine like terms: 96 + -288 = -192
-192 + 40x + 4x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-192 + 40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-48 + 10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-48 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + 10x + x2 = 0

Solving
-48 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 10x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 10x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 10x + x2 = 0 + 48
10x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
10x + x2 = 48

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 = 48 + 25

Reorder the terms:
25 + 10x + x2 = 48 + 25

Combine like terms: 48 + 25 = 73
25 + 10x + x2 = 73

Factor a perfect square on the left side:
(x + 5)(x + 5) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 5) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + 5 = 8.544003745

Simplifying
x + 5 = 8.544003745

Reorder the terms:
5 + x = 8.544003745

Solving
5 + x = 8.544003745

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 = 8.544003745 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.544003745 + -5
x = 8.544003745 + -5

Combine like terms: 8.544003745 + -5 = 3.544003745
x = 3.544003745

Simplifying
x = 3.544003745


Subproblem 2
x + 5 = -8.544003745

Simplifying
x + 5 = -8.544003745

Reorder the terms:
5 + x = -8.544003745

Solving
5 + x = -8.544003745

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 = -8.544003745 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.544003745 + -5
x = -8.544003745 + -5

Combine like terms: -8.544003745 + -5 = -13.544003745
x = -13.544003745

Simplifying
x = -13.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.544003745, -13.544003745}
Solution
x = {3.544003745, -13.544003745}

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