(2x+4)(x+1)=52

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Solution for (2x+4)(x+1)=52 equation: 


Simplifying
(2x + 4)(x + 1) = 52

Reorder the terms:
(4 + 2x)(x + 1) = 52

Reorder the terms:
(4 + 2x)(1 + x) = 52

Multiply (4 + 2x) * (1 + x)
(4(1 + x) + 2x * (1 + x)) = 52
((1 * 4 + x * 4) + 2x * (1 + x)) = 52
((4 + 4x) + 2x * (1 + x)) = 52
(4 + 4x + (1 * 2x + x * 2x)) = 52
(4 + 4x + (2x + 2x2)) = 52

Combine like terms: 4x + 2x = 6x
(4 + 6x + 2x2) = 52

Solving
4 + 6x + 2x2 = 52

Solving for variable 'x'.

Reorder the terms:
4 + -52 + 6x + 2x2 = 52 + -52

Combine like terms: 4 + -52 = -48
-48 + 6x + 2x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-48 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 3x + x2 = 0

Solving
-24 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 3x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 3x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 3x + x2 = 0 + 24
3x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
3x + x2 = 24

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 = 24 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 24 + 2.25

Combine like terms: 24 + 2.25 = 26.25
2.25 + 3x + x2 = 26.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
x + 1.5 = 5.123475383

Simplifying
x + 1.5 = 5.123475383

Reorder the terms:
1.5 + x = 5.123475383

Solving
1.5 + x = 5.123475383

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 = 5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.123475383 + -1.5
x = 5.123475383 + -1.5

Combine like terms: 5.123475383 + -1.5 = 3.623475383
x = 3.623475383

Simplifying
x = 3.623475383


Subproblem 2
x + 1.5 = -5.123475383

Simplifying
x + 1.5 = -5.123475383

Reorder the terms:
1.5 + x = -5.123475383

Solving
1.5 + x = -5.123475383

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 = -5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.123475383 + -1.5
x = -5.123475383 + -1.5

Combine like terms: -5.123475383 + -1.5 = -6.623475383
x = -6.623475383

Simplifying
x = -6.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.623475383, -6.623475383}
Solution
x = {3.623475383, -6.623475383}

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