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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) = 0Subproblem 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 = 2.5zSubproblem 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 = -0.3333333333zSolution
y = {2.5z, -0.3333333333z}
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