3x^2+12x+6x+24=240

Solution for 3x^2+12x+6x+24=240 equation:

Simplifying
3x2 + 12x + 6x + 24 = 240

Reorder the terms:
24 + 12x + 6x + 3x2 = 240

Combine like terms: 12x + 6x = 18x
24 + 18x + 3x2 = 240

Solving
24 + 18x + 3x2 = 240

Solving for variable 'x'.

Reorder the terms:
24 + -240 + 18x + 3x2 = 240 + -240

Combine like terms: 24 + -240 = -216
-216 + 18x + 3x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-216 + 18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-72 + 6x + x2) = 0

Factor a trinomial.
3((-12 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-12, 6}