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Simplifying 3y2 + 2yz + -1z2 = 0 Reorder the terms: 2yz + 3y2 + -1z2 = 0 Solving 2yz + 3y2 + -1z2 = 0 Solving for variable 'y'. Factor a trinomial. (3y + -1z)(y + z) = 0Subproblem 1
Set the factor '(3y + -1z)' equal to zero and attempt to solve: Simplifying 3y + -1z = 0 Solving 3y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 3y + -1z + z = 0 + z Combine like terms: -1z + z = 0 3y + 0 = 0 + z 3y = 0 + z Remove the zero: 3y = z Divide each side by '3'. y = 0.3333333333z Simplifying y = 0.3333333333zSubproblem 2
Set the factor '(y + z)' equal to zero and attempt to solve: Simplifying y + z = 0 Solving y + z = 0 Move all terms containing y to the left, all other terms to the right. Add '-1z' to each side of the equation. y + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 y + 0 = 0 + -1z y = 0 + -1z Remove the zero: y = -1z Simplifying y = -1zSolution
y = {0.3333333333z, -1z}
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