-3x^3-27x^2-54x=0

Solution for -3x^3-27x^2-54x=0 equation:

Simplifying
-3x3 + -27x2 + -54x = 0

Reorder the terms:
-54x + -27x2 + -3x3 = 0

Solving
-54x + -27x2 + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3x'.
-3x(18 + 9x + x2) = 0

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

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {0, -6, -3}