y^3z+y^2z^2-6yz^3=

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Solution for y^3z+y^2z^2-6yz^3= equation: 


Simplifying
y3z + y2z2 + -6yz3 = 0

Reorder the terms:
-6yz3 + y2z2 + y3z = 0

Solving
-6yz3 + y2z2 + y3z = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'yz'.
yz(-6z2 + yz + y2) = 0

Factor a trinomial.
yz((-3z + -1y)(2z + -1y)) = 0


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

Simplifying
yz = 0

Solving
yz = 0

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

Simplifying
yz = 0

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

Simplifying
-3z + -1y = 0

Reorder the terms:
-1y + -3z = 0

Solving
-1y + -3z = 0

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

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

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

Divide each side by '-1'.
y = -3z

Simplifying
y = -3z

Subproblem 3
Set the factor '(2z + -1y)' equal to zero and attempt to solve:

Simplifying
2z + -1y = 0

Reorder the terms:
-1y + 2z = 0

Solving
-1y + 2z = 0

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

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

Combine like terms: 2z + -2z = 0
-1y + 0 = 0 + -2z
-1y = 0 + -2z
Remove the zero:
-1y = -2z

Divide each side by '-1'.
y = 2z

Simplifying
y = 2z
Solution
y = {-3z, 2z}

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