8y^2-10yz-3z^2=0

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Solution for 8y^2-10yz-3z^2=0 equation: 


Simplifying
8y2 + -10yz + -3z2 = 0

Reorder the terms:
-10yz + 8y2 + -3z2 = 0

Solving
-10yz + 8y2 + -3z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2y + -3z)(4y + z) = 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 '(4y + z)' equal to zero and attempt to solve:

Simplifying
4y + z = 0

Solving
4y + z = 0

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

Add '-1z' to each side of the equation.
4y + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
4y + 0 = 0 + -1z
4y = 0 + -1z
Remove the zero:
4y = -1z

Divide each side by '4'.
y = -0.25z

Simplifying
y = -0.25z
Solution
y = {1.5z, -0.25z}

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