3x^2z+27xz+54z=

Solution for 3x^2z+27xz+54z= equation:

Simplifying
3x2z + 27xz + 54z = 0

Reorder the terms:
27xz + 3x2z + 54z = 0

Solving
27xz + 3x2z + 54z = 0

Solving for variable 'x'.

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

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

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

Simplifying
z = 0

Solving
z = 0

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

Add '-1z' to each side of the equation.
z + -1z = 0 + -1z
Remove the zero:
0 = -1z

Simplifying
0 = -1z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(x + 3)' equal to zero and attempt to solve:

Simplifying
x + 3 = 0

Reorder the terms:
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
Subproblem 3
Set the factor '(x + 6)' equal to zero and attempt to solve:

Simplifying
x + 6 = 0

Reorder the terms:
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 = {-3, -6}