y^2-35yz+150z^2=0

Solution for y^2-35yz+150z^2=0 equation:

Simplifying
y2 + -35yz + 150z2 = 0

Reorder the terms:
-35yz + y2 + 150z2 = 0

Solving
-35yz + y2 + 150z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(y + -30z)(y + -5z) = 0

Subproblem 1
Set the factor '(y + -30z)' equal to zero and attempt to solve:

Simplifying
y + -30z = 0

Solving
y + -30z = 0

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

Add '30z' to each side of the equation.
y + -30z + 30z = 0 + 30z

Combine like terms: -30z + 30z = 0
y + 0 = 0 + 30z
y = 0 + 30z
Remove the zero:
y = 30z

Simplifying
y = 30z
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 = {30z, 5z}