(4+2x)(6+2x)=96

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Solution for (4+2x)(6+2x)=96 equation: 


Simplifying
(4 + 2x)(6 + 2x) = 96

Multiply (4 + 2x) * (6 + 2x)
(4(6 + 2x) + 2x * (6 + 2x)) = 96
((6 * 4 + 2x * 4) + 2x * (6 + 2x)) = 96
((24 + 8x) + 2x * (6 + 2x)) = 96
(24 + 8x + (6 * 2x + 2x * 2x)) = 96
(24 + 8x + (12x + 4x2)) = 96

Combine like terms: 8x + 12x = 20x
(24 + 20x + 4x2) = 96

Solving
24 + 20x + 4x2 = 96

Solving for variable 'x'.

Reorder the terms:
24 + -96 + 20x + 4x2 = 96 + -96

Combine like terms: 24 + -96 = -72
-72 + 20x + 4x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-72 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + 5x + x2 = 0

Solving
-18 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 5x + x2 = 0 + 18
5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
5x + x2 = 18

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 = 18 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + 5x + x2 = 24.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + 2.5 = 4.924428901

Simplifying
x + 2.5 = 4.924428901

Reorder the terms:
2.5 + x = 4.924428901

Solving
2.5 + x = 4.924428901

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 = 4.924428901 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.924428901 + -2.5
x = 4.924428901 + -2.5

Combine like terms: 4.924428901 + -2.5 = 2.424428901
x = 2.424428901

Simplifying
x = 2.424428901


Subproblem 2
x + 2.5 = -4.924428901

Simplifying
x + 2.5 = -4.924428901

Reorder the terms:
2.5 + x = -4.924428901

Solving
2.5 + x = -4.924428901

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 = -4.924428901 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.924428901 + -2.5
x = -4.924428901 + -2.5

Combine like terms: -4.924428901 + -2.5 = -7.424428901
x = -7.424428901

Simplifying
x = -7.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.424428901, -7.424428901}
Solution
x = {2.424428901, -7.424428901}

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