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Simplifying 42y2 + -13yz + -42z2 = 0 Reorder the terms: -13yz + 42y2 + -42z2 = 0 Solving -13yz + 42y2 + -42z2 = 0 Solving for variable 'y'. Factor a trinomial. (6y + -7z)(7y + 6z) = 0Subproblem 1
Set the factor '(6y + -7z)' equal to zero and attempt to solve: Simplifying 6y + -7z = 0 Solving 6y + -7z = 0 Move all terms containing y to the left, all other terms to the right. Add '7z' to each side of the equation. 6y + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 6y + 0 = 0 + 7z 6y = 0 + 7z Remove the zero: 6y = 7z Divide each side by '6'. y = 1.166666667z Simplifying y = 1.166666667zSubproblem 2
Set the factor '(7y + 6z)' equal to zero and attempt to solve: Simplifying 7y + 6z = 0 Solving 7y + 6z = 0 Move all terms containing y to the left, all other terms to the right. Add '-6z' to each side of the equation. 7y + 6z + -6z = 0 + -6z Combine like terms: 6z + -6z = 0 7y + 0 = 0 + -6z 7y = 0 + -6z Remove the zero: 7y = -6z Divide each side by '7'. y = -0.8571428571z Simplifying y = -0.8571428571zSolution
y = {1.166666667z, -0.8571428571z}
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