6y^2-13yz-5z^2=0

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Solution for 6y^2-13yz-5z^2=0 equation: 


Simplifying
6y2 + -13yz + -5z2 = 0

Reorder the terms:
-13yz + 6y2 + -5z2 = 0

Solving
-13yz + 6y2 + -5z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2y + -5z)(3y + z) = 0


Subproblem 1
Set the factor '(2y + -5z)' equal to zero and attempt to solve:

Simplifying
2y + -5z = 0

Solving
2y + -5z = 0

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

Add '5z' to each side of the equation.
2y + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
2y + 0 = 0 + 5z
2y = 0 + 5z
Remove the zero:
2y = 5z

Divide each side by '2'.
y = 2.5z

Simplifying
y = 2.5z

Subproblem 2
Set the factor '(3y + z)' equal to zero and attempt to solve:

Simplifying
3y + z = 0

Solving
3y + z = 0

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

Add '-1z' to each side of the equation.
3y + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
3y + 0 = 0 + -1z
3y = 0 + -1z
Remove the zero:
3y = -1z

Divide each side by '3'.
y = -0.3333333333z

Simplifying
y = -0.3333333333z
Solution
y = {2.5z, -0.3333333333z}

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