(2x+4)(x+3)=56

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Solution for (2x+4)(x+3)=56 equation: 


Simplifying
(2x + 4)(x + 3) = 56

Reorder the terms:
(4 + 2x)(x + 3) = 56

Reorder the terms:
(4 + 2x)(3 + x) = 56

Multiply (4 + 2x) * (3 + x)
(4(3 + x) + 2x * (3 + x)) = 56
((3 * 4 + x * 4) + 2x * (3 + x)) = 56
((12 + 4x) + 2x * (3 + x)) = 56
(12 + 4x + (3 * 2x + x * 2x)) = 56
(12 + 4x + (6x + 2x2)) = 56

Combine like terms: 4x + 6x = 10x
(12 + 10x + 2x2) = 56

Solving
12 + 10x + 2x2 = 56

Solving for variable 'x'.

Reorder the terms:
12 + -56 + 10x + 2x2 = 56 + -56

Combine like terms: 12 + -56 = -44
-44 + 10x + 2x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-44 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-22 + 5x + x2 = 0

Solving
-22 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 5x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 5x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 5x + x2 = 0 + 22
5x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
5x + x2 = 22

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 = 22 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 22 + 6.25

Combine like terms: 22 + 6.25 = 28.25
6.25 + 5x + x2 = 28.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
x + 2.5 = 5.315072906

Simplifying
x + 2.5 = 5.315072906

Reorder the terms:
2.5 + x = 5.315072906

Solving
2.5 + x = 5.315072906

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 = 5.315072906 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.315072906 + -2.5
x = 5.315072906 + -2.5

Combine like terms: 5.315072906 + -2.5 = 2.815072906
x = 2.815072906

Simplifying
x = 2.815072906


Subproblem 2
x + 2.5 = -5.315072906

Simplifying
x + 2.5 = -5.315072906

Reorder the terms:
2.5 + x = -5.315072906

Solving
2.5 + x = -5.315072906

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 = -5.315072906 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.315072906 + -2.5
x = -5.315072906 + -2.5

Combine like terms: -5.315072906 + -2.5 = -7.815072906
x = -7.815072906

Simplifying
x = -7.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.815072906, -7.815072906}
Solution
x = {2.815072906, -7.815072906}

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