27x^2z+36xz+12z=0

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Solution for 27x^2z+36xz+12z=0 equation: 


Simplifying
27x2z + 36xz + 12z = 0

Reorder the terms:
36xz + 27x2z + 12z = 0

Solving
36xz + 27x2z + 12z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(12x + 9x2 + 4) = 0

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

Simplifying
3x + 2 = 0

Reorder the terms:
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
3x + 2 = 0

Reorder the terms:
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-0.6666666667, -0.6666666667}

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