6w^2z+39wz+18z=

Solution for 6w^2z+39wz+18z= equation:

Simplifying
6w2z + 39wz + 18z = 0

Reorder the terms:
39wz + 6w2z + 18z = 0

Solving
39wz + 6w2z + 18z = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(13w + 2w2 + 6) = 0

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

Simplifying
2w + 1 = 0

Reorder the terms:
1 + 2w = 0

Solving
1 + 2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 3
Set the factor '(w + 6)' equal to zero and attempt to solve:

Simplifying
w + 6 = 0

Reorder the terms:
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

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

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

Simplifying
w = -6
Solution
w = {-0.5, -6}