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Simplifying 8y2 + -58yz + 60z2 = 0 Reorder the terms: -58yz + 8y2 + 60z2 = 0 Solving -58yz + 8y2 + 60z2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-29yz + 4y2 + 30z2) = 0 Factor a trinomial. 2((y + -6z)(4y + -5z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(y + -6z)' equal to zero and attempt to solve: Simplifying y + -6z = 0 Solving y + -6z = 0 Move all terms containing y to the left, all other terms to the right. Add '6z' to each side of the equation. y + -6z + 6z = 0 + 6z Combine like terms: -6z + 6z = 0 y + 0 = 0 + 6z y = 0 + 6z Remove the zero: y = 6z Simplifying y = 6zSubproblem 2
Set the factor '(4y + -5z)' equal to zero and attempt to solve: Simplifying 4y + -5z = 0 Solving 4y + -5z = 0 Move all terms containing y to the left, all other terms to the right. Add '5z' to each side of the equation. 4y + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 4y + 0 = 0 + 5z 4y = 0 + 5z Remove the zero: 4y = 5z Divide each side by '4'. y = 1.25z Simplifying y = 1.25zSolution
y = {6z, 1.25z}
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