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

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

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

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

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

Multiply (6 + 3x) * (3 + x)
(6(3 + x) + 3x * (3 + x)) = 60
((3 * 6 + x * 6) + 3x * (3 + x)) = 60
((18 + 6x) + 3x * (3 + x)) = 60
(18 + 6x + (3 * 3x + x * 3x)) = 60
(18 + 6x + (9x + 3x2)) = 60

Combine like terms: 6x + 9x = 15x
(18 + 15x + 3x2) = 60

Solving
18 + 15x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
18 + -60 + 15x + 3x2 = 60 + -60

Combine like terms: 18 + -60 = -42
-42 + 15x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-42 + 15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(2 + -1x)) = 0

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7, 2}