y^3z+3y^2z^2-54yz^3=0

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Solution for y^3z+3y^2z^2-54yz^3=0 equation: 


Simplifying
y3z + 3y2z2 + -54yz3 = 0

Reorder the terms:
-54yz3 + 3y2z2 + y3z = 0

Solving
-54yz3 + 3y2z2 + y3z = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'yz'.
yz(-54z2 + 3yz + y2) = 0

Factor a trinomial.
yz((-9z + -1y)(6z + -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 '(-9z + -1y)' equal to zero and attempt to solve:

Simplifying
-9z + -1y = 0

Reorder the terms:
-1y + -9z = 0

Solving
-1y + -9z = 0

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

Add '9z' to each side of the equation.
-1y + -9z + 9z = 0 + 9z

Combine like terms: -9z + 9z = 0
-1y + 0 = 0 + 9z
-1y = 0 + 9z
Remove the zero:
-1y = 9z

Divide each side by '-1'.
y = -9z

Simplifying
y = -9z

Subproblem 3
Set the factor '(6z + -1y)' equal to zero and attempt to solve:

Simplifying
6z + -1y = 0

Reorder the terms:
-1y + 6z = 0

Solving
-1y + 6z = 0

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

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

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

Divide each side by '-1'.
y = 6z

Simplifying
y = 6z
Solution
y = {-9z, 6z}

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