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

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


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

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

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

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(2y + -3z)' equal to zero and attempt to solve:

Simplifying
2y + -3z = 0

Solving
2y + -3z = 0

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

Add '3z' to each side of the equation.
2y + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
2y + 0 = 0 + 3z
2y = 0 + 3z
Remove the zero:
2y = 3z

Divide each side by '2'.
y = 1.5z

Simplifying
y = 1.5z

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

Simplifying
3y + 2z = 0

Solving
3y + 2z = 0

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

Add '-2z' to each side of the equation.
3y + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
3y + 0 = 0 + -2z
3y = 0 + -2z
Remove the zero:
3y = -2z

Divide each side by '3'.
y = -0.6666666667z

Simplifying
y = -0.6666666667z
Solution
y = {1.5z, -0.6666666667z}

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