z^6+3z^5y-18z^4y^2=

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Solution for z^6+3z^5y-18z^4y^2= equation: 


Simplifying
z6 + 3z5y + -18z4y2 = 0

Reorder the terms:
3yz5 + -18y2z4 + z6 = 0

Solving
3yz5 + -18y2z4 + z6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'z4'.
z4(3yz + -18y2 + z2) = 0

Factor a trinomial.
z4((-6y + -1z)(3y + -1z)) = 0


Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

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

Add '-1z4' to each side of the equation.
z4 + -1z4 = 0 + -1z4
Remove the zero:
0 = -1z4

Simplifying
0 = -1z4

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 '(-6y + -1z)' equal to zero and attempt to solve:

Simplifying
-6y + -1z = 0

Solving
-6y + -1z = 0

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

Add 'z' to each side of the equation.
-6y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
-6y + 0 = 0 + z
-6y = 0 + z
Remove the zero:
-6y = z

Divide each side by '-6'.
y = -0.1666666667z

Simplifying
y = -0.1666666667z

Subproblem 3
Set the factor '(3y + -1z)' equal to zero and attempt to solve:

Simplifying
3y + -1z = 0

Solving
3y + -1z = 0

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

Add 'z' to each side of the equation.
3y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
3y + 0 = 0 + z
3y = 0 + z
Remove the zero:
3y = z

Divide each side by '3'.
y = 0.3333333333z

Simplifying
y = 0.3333333333z
Solution
y = {-0.1666666667z, 0.3333333333z}

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