42z^2-zy-y^2=

Solution for 42z^2-zy-y^2= equation:

Simplifying
42z2 + -1zy + -1y2 = 0

Reorder the terms:
-1yz + -1y2 + 42z2 = 0

Solving
-1yz + -1y2 + 42z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1y + -7z)(y + -6z) = 0

Subproblem 1
Set the factor '(-1y + -7z)' equal to zero and attempt to solve:

Simplifying
-1y + -7z = 0

Solving
-1y + -7z = 0

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

Add '7z' to each side of the equation.
-1y + -7z + 7z = 0 + 7z

Combine like terms: -7z + 7z = 0
-1y + 0 = 0 + 7z
-1y = 0 + 7z
Remove the zero:
-1y = 7z

Divide each side by '-1'.
y = -7z

Simplifying
y = -7z
Subproblem 2
Set the factor '(y + -6z)' equal to zero and attempt to solve:

Simplifying
y + -6z = 0

Solving
y + -6z = 0

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

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

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

Simplifying
y = 6z
Solution
y = {-7z, 6z}