(2x+4)(x+5)=60

Solution for (2x+4)(x+5)=60 equation:

Simplifying
(2x + 4)(x + 5) = 60

Reorder the terms:
(4 + 2x)(x + 5) = 60

Reorder the terms:
(4 + 2x)(5 + x) = 60

Multiply (4 + 2x) * (5 + x)
(4(5 + x) + 2x * (5 + x)) = 60
((5 * 4 + x * 4) + 2x * (5 + x)) = 60
((20 + 4x) + 2x * (5 + x)) = 60
(20 + 4x + (5 * 2x + x * 2x)) = 60
(20 + 4x + (10x + 2x2)) = 60

Combine like terms: 4x + 10x = 14x
(20 + 14x + 2x2) = 60

Solving
20 + 14x + 2x2 = 60

Solving for variable 'x'.

Reorder the terms:
20 + -60 + 14x + 2x2 = 60 + -60

Combine like terms: 20 + -60 = -40
-40 + 14x + 2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-40 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 7x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 7x + x2 = 0

Solving
-20 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 7x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 7x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 7x + x2 = 0 + 20
7x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
7x + x2 = 20

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 = 20 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 20 + 12.25

Combine like terms: 20 + 12.25 = 32.25
12.25 + 7x + x2 = 32.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 3.5 = 5.678908346

Simplifying
x + 3.5 = 5.678908346

Reorder the terms:
3.5 + x = 5.678908346

Solving
3.5 + x = 5.678908346

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 = 5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.678908346 + -3.5
x = 5.678908346 + -3.5

Combine like terms: 5.678908346 + -3.5 = 2.178908346
x = 2.178908346

Simplifying
x = 2.178908346

Subproblem 2
x + 3.5 = -5.678908346

Simplifying
x + 3.5 = -5.678908346

Reorder the terms:
3.5 + x = -5.678908346

Solving
3.5 + x = -5.678908346

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 = -5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.678908346 + -3.5
x = -5.678908346 + -3.5

Combine like terms: -5.678908346 + -3.5 = -9.178908346
x = -9.178908346

Simplifying
x = -9.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.178908346, -9.178908346}
Solution
x = {2.178908346, -9.178908346}