30z^2-zy-y^2=0

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Solution for 30z^2-zy-y^2=0 equation: 


Simplifying
30z2 + -1zy + -1y2 = 0

Reorder the terms:
-1yz + -1y2 + 30z2 = 0

Solving
-1yz + -1y2 + 30z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1y + -6z)(y + -5z) = 0


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

Simplifying
-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

Subproblem 2
Set the factor '(y + -5z)' equal to zero and attempt to solve:

Simplifying
y + -5z = 0

Solving
y + -5z = 0

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

Add '5z' to each side of the equation.
y + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
y + 0 = 0 + 5z
y = 0 + 5z
Remove the zero:
y = 5z

Simplifying
y = 5z
Solution
y = {-6z, 5z}

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