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

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

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

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

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

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

Combine like terms: 2x + 3x = 5x
3(6 + 5x + x2) = 60
(6 * 3 + 5x * 3 + x2 * 3) = 60
(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}