9y^2-25yz-6z^2=0

Solution for 9y^2-25yz-6z^2=0 equation:

Simplifying
9y2 + -25yz + -6z2 = 0

Reorder the terms:
-25yz + 9y2 + -6z2 = 0

Solving
-25yz + 9y2 + -6z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(y + -3z)(9y + 2z) = 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 '(9y + 2z)' equal to zero and attempt to solve:

Simplifying
9y + 2z = 0

Solving
9y + 2z = 0

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

Add '-2z' to each side of the equation.
9y + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
9y + 0 = 0 + -2z
9y = 0 + -2z
Remove the zero:
9y = -2z

Divide each side by '9'.
y = -0.2222222222z

Simplifying
y = -0.2222222222z
Solution
y = {3z, -0.2222222222z}