y^2-6yz+9z^2=0

Solution for y^2-6yz+9z^2=0 equation:

Simplifying
y2 + -6yz + 9z2 = 0

Reorder the terms:
-6yz + y2 + 9z2 = 0

Solving
-6yz + y2 + 9z2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
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 = {3z, 3z}