12z^2-zy-y^2=0

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Solution for 12z^2-zy-y^2=0 equation: 


Simplifying
12z2 + -1zy + -1y2 = 0

Reorder the terms:
-1yz + -1y2 + 12z2 = 0

Solving
-1yz + -1y2 + 12z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1y + -4z)(y + -3z) = 0


Subproblem 1
Set the factor '(-1y + -4z)' equal to zero and attempt to solve:

Simplifying
-1y + -4z = 0

Solving
-1y + -4z = 0

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

Add '4z' to each side of the equation.
-1y + -4z + 4z = 0 + 4z

Combine like terms: -4z + 4z = 0
-1y + 0 = 0 + 4z
-1y = 0 + 4z
Remove the zero:
-1y = 4z

Divide each side by '-1'.
y = -4z

Simplifying
y = -4z

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

Simplifying
y + -3z = 0

Solving
y + -3z = 0

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

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

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

Simplifying
y = 3z
Solution
y = {-4z, 3z}

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