3(x^2+15x+54)=0

Solution for 3(x^2+15x+54)=0 equation:

Simplifying
3(x2 + 15x + 54) = 0

Reorder the terms:
3(54 + 15x + x2) = 0
(54 * 3 + 15x * 3 + x2 * 3) = 0
(162 + 45x + 3x2) = 0

Solving
162 + 45x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(54 + 15x + x2) = 0

Factor a trinomial.
3((9 + x)(6 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-9, -6}