240=(x+5)(2x+4)

Solution for 240=(x+5)(2x+4) equation:

Simplifying
240 = (x + 5)(2x + 4)

Reorder the terms:
240 = (5 + x)(2x + 4)

Reorder the terms:
240 = (5 + x)(4 + 2x)

Multiply (5 + x) * (4 + 2x)
240 = (5(4 + 2x) + x(4 + 2x))
240 = ((4 * 5 + 2x * 5) + x(4 + 2x))
240 = ((20 + 10x) + x(4 + 2x))
240 = (20 + 10x + (4 * x + 2x * x))
240 = (20 + 10x + (4x + 2x2))

Combine like terms: 10x + 4x = 14x
240 = (20 + 14x + 2x2)

Solving
240 = 20 + 14x + 2x2

Solving for variable 'x'.

Combine like terms: 240 + -20 = 220
220 + -14x + -2x2 = 20 + 14x + 2x2 + -20 + -14x + -2x2

Reorder the terms:
220 + -14x + -2x2 = 20 + -20 + 14x + -14x + 2x2 + -2x2

Combine like terms: 20 + -20 = 0
220 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2
220 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
220 + -14x + -2x2 = 0 + 2x2 + -2x2
220 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
220 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(110 + -7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(110 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
110 + -7x + -1x2 = 0

Solving
110 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-110 + 7x + x2 = 0

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 7x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + 7x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 7x + x2 = 0 + 110
7x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
7x + x2 = 110

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 110 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 110 + 12.25

Combine like terms: 110 + 12.25 = 122.25
12.25 + 7x + x2 = 122.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(x + 3.5) equal to 11.056672194 and -11.056672194.

Subproblem 1
x + 3.5 = 11.056672194

Simplifying
x + 3.5 = 11.056672194

Reorder the terms:
3.5 + x = 11.056672194

Solving
3.5 + x = 11.056672194

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 11.056672194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 11.056672194 + -3.5
x = 11.056672194 + -3.5

Combine like terms: 11.056672194 + -3.5 = 7.556672194
x = 7.556672194

Simplifying
x = 7.556672194

Subproblem 2
x + 3.5 = -11.056672194

Simplifying
x + 3.5 = -11.056672194

Reorder the terms:
3.5 + x = -11.056672194

Solving
3.5 + x = -11.056672194

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -11.056672194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -11.056672194 + -3.5
x = -11.056672194 + -3.5

Combine like terms: -11.056672194 + -3.5 = -14.556672194
x = -14.556672194

Simplifying
x = -14.556672194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.556672194, -14.556672194}
Solution
x = {7.556672194, -14.556672194}