(x+2)(x)(3)=240

Solution for (x+2)(x)(3)=240 equation:

Simplifying
(x + 2)(x)(3) = 240

Reorder the terms:
(2 + x)(x)(3) = 240

Reorder the terms for easier multiplication:
3x(2 + x) = 240
(2 * 3x + x * 3x) = 240
(6x + 3x2) = 240

Solving
6x + 3x2 = 240

Solving for variable 'x'.

Reorder the terms:
-240 + 6x + 3x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-80 + 2x + x2) = 0

Factor a trinomial.
3((-10 + -1x)(8 + -1x)) = 0

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

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-10, 8}