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Simplifying 12y2 + -5yz + -2z2 = 0 Reorder the terms: -5yz + 12y2 + -2z2 = 0 Solving -5yz + 12y2 + -2z2 = 0 Solving for variable 'y'. Factor a trinomial. (3y + -2z)(4y + z) = 0Subproblem 1
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 = 0.6666666667zSubproblem 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 = -0.25zSolution
y = {0.6666666667z, -0.25z}
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