y^2-6yz+5z^2=0

Solution for y^2-6yz+5z^2=0 equation:

Simplifying
y2 + -6yz + 5z2 = 0

Reorder the terms:
-6yz + y2 + 5z2 = 0

Solving
-6yz + y2 + 5z2 = 0

Solving for variable 'y'.

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

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

Simplifying
y + -1z = 0

Solving
y + -1z = 0

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

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

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

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