(x+2)(2x+3)=60

Solution for (x+2)(2x+3)=60 equation:

Simplifying
(x + 2)(2x + 3) = 60

Reorder the terms:
(2 + x)(2x + 3) = 60

Reorder the terms:
(2 + x)(3 + 2x) = 60

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = 60
((3 * 2 + 2x * 2) + x(3 + 2x)) = 60
((6 + 4x) + x(3 + 2x)) = 60
(6 + 4x + (3 * x + 2x * x)) = 60
(6 + 4x + (3x + 2x2)) = 60

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = 60

Solving
6 + 7x + 2x2 = 60

Solving for variable 'x'.

Reorder the terms:
6 + -60 + 7x + 2x2 = 60 + -60

Combine like terms: 6 + -60 = -54
-54 + 7x + 2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-54 + 7x + 2x2 = 0

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

Divide each side by '2'.
-27 + 3.5x + x2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 3.5x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 3.5x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 3.5x + x2 = 0 + 27
3.5x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
3.5x + x2 = 27

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 27 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 27 + 3.0625

Combine like terms: 27 + 3.0625 = 30.0625
3.0625 + 3.5x + x2 = 30.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(x + 1.75) equal to 5.48292805 and -5.48292805.

Subproblem 1
x + 1.75 = 5.48292805

Simplifying
x + 1.75 = 5.48292805

Reorder the terms:
1.75 + x = 5.48292805

Solving
1.75 + x = 5.48292805

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 5.48292805 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 5.48292805 + -1.75
x = 5.48292805 + -1.75

Combine like terms: 5.48292805 + -1.75 = 3.73292805
x = 3.73292805

Simplifying
x = 3.73292805

Subproblem 2
x + 1.75 = -5.48292805

Simplifying
x + 1.75 = -5.48292805

Reorder the terms:
1.75 + x = -5.48292805

Solving
1.75 + x = -5.48292805

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -5.48292805 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -5.48292805 + -1.75
x = -5.48292805 + -1.75

Combine like terms: -5.48292805 + -1.75 = -7.23292805
x = -7.23292805

Simplifying
x = -7.23292805

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.73292805, -7.23292805}