10y^2-13yz-3z^2=0

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Solution for 10y^2-13yz-3z^2=0 equation:


Simplifying
10y2 + -13yz + -3z2 = 0

Reorder the terms:
-13yz + 10y2 + -3z2 = 0

Solving
-13yz + 10y2 + -3z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2y + -3z)(5y + 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 '(5y + z)' equal to zero and attempt to solve: Simplifying 5y + z = 0 Solving 5y + z = 0 Move all terms containing y to the left, all other terms to the right. Add '-1z' to each side of the equation. 5y + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 5y + 0 = 0 + -1z 5y = 0 + -1z Remove the zero: 5y = -1z Divide each side by '5'. y = -0.2z Simplifying y = -0.2z

Solution

y = {1.5z, -0.2z}

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