3x^2z+9xz+6z=0

Solution for 3x^2z+9xz+6z=0 equation:

Simplifying
3x2z + 9xz + 6z = 0

Reorder the terms:
9xz + 3x2z + 6z = 0

Solving
9xz + 3x2z + 6z = 0

Solving for variable 'x'.

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

Factor a trinomial.
3z((x + 1)(x + 2)) = 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 + 1)' equal to zero and attempt to solve:

Simplifying
x + 1 = 0

Reorder the terms:
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 3
Set the factor '(x + 2)' equal to zero and attempt to solve:

Simplifying
x + 2 = 0

Reorder the terms:
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-1, -2}