60=(x+5)(3x+6)

Solution for 60=(x+5)(3x+6) equation:

Simplifying
60 = (x + 5)(3x + 6)

Reorder the terms:
60 = (5 + x)(3x + 6)

Reorder the terms:
60 = (5 + x)(6 + 3x)

Multiply (5 + x) * (6 + 3x)
60 = (5(6 + 3x) + x(6 + 3x))
60 = ((6 * 5 + 3x * 5) + x(6 + 3x))
60 = ((30 + 15x) + x(6 + 3x))
60 = (30 + 15x + (6 * x + 3x * x))
60 = (30 + 15x + (6x + 3x2))

Combine like terms: 15x + 6x = 21x
60 = (30 + 21x + 3x2)

Solving
60 = 30 + 21x + 3x2

Solving for variable 'x'.

Combine like terms: 60 + -30 = 30
30 + -21x + -3x2 = 30 + 21x + 3x2 + -30 + -21x + -3x2

Reorder the terms:
30 + -21x + -3x2 = 30 + -30 + 21x + -21x + 3x2 + -3x2

Combine like terms: 30 + -30 = 0
30 + -21x + -3x2 = 0 + 21x + -21x + 3x2 + -3x2
30 + -21x + -3x2 = 21x + -21x + 3x2 + -3x2

Combine like terms: 21x + -21x = 0
30 + -21x + -3x2 = 0 + 3x2 + -3x2
30 + -21x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
30 + -21x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -7x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(10 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -7x + -1x2 = 0

Solving
10 + -7x + -1x2 = 0

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

Divide each side by '-1'.
-10 + 7x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 7x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 7x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7x + x2 = 0 + 10
7x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
7x + x2 = 10

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 = 10 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7x + x2 = 22.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + 3.5 = 4.716990566

Simplifying
x + 3.5 = 4.716990566

Reorder the terms:
3.5 + x = 4.716990566

Solving
3.5 + x = 4.716990566

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 = 4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.716990566 + -3.5
x = 4.716990566 + -3.5

Combine like terms: 4.716990566 + -3.5 = 1.216990566
x = 1.216990566

Simplifying
x = 1.216990566

Subproblem 2
x + 3.5 = -4.716990566

Simplifying
x + 3.5 = -4.716990566

Reorder the terms:
3.5 + x = -4.716990566

Solving
3.5 + x = -4.716990566

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 = -4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.716990566 + -3.5
x = -4.716990566 + -3.5

Combine like terms: -4.716990566 + -3.5 = -8.216990566
x = -8.216990566

Simplifying
x = -8.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.216990566, -8.216990566}
Solution
x = {1.216990566, -8.216990566}