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Simplifying 0 = 9y2 + 24yz + 16z2 Reorder the terms: 0 = 24yz + 9y2 + 16z2 Solving 0 = 24yz + 9y2 + 16z2 Solving for variable 'y'. Remove the zero: -24yz + -9y2 + -16z2 = 24yz + 9y2 + 16z2 + -24yz + -9y2 + -16z2 Reorder the terms: -24yz + -9y2 + -16z2 = 24yz + -24yz + 9y2 + -9y2 + 16z2 + -16z2 Combine like terms: 24yz + -24yz = 0 -24yz + -9y2 + -16z2 = 0 + 9y2 + -9y2 + 16z2 + -16z2 -24yz + -9y2 + -16z2 = 9y2 + -9y2 + 16z2 + -16z2 Combine like terms: 9y2 + -9y2 = 0 -24yz + -9y2 + -16z2 = 0 + 16z2 + -16z2 -24yz + -9y2 + -16z2 = 16z2 + -16z2 Combine like terms: 16z2 + -16z2 = 0 -24yz + -9y2 + -16z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24yz + 9y2 + 16z2) = 0 Factor a trinomial. -1((3y + 4z)(3y + 4z)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3y + 4z)' equal to zero and attempt to solve: Simplifying 3y + 4z = 0 Solving 3y + 4z = 0 Move all terms containing y to the left, all other terms to the right. Add '-4z' to each side of the equation. 3y + 4z + -4z = 0 + -4z Combine like terms: 4z + -4z = 0 3y + 0 = 0 + -4z 3y = 0 + -4z Remove the zero: 3y = -4z Divide each side by '3'. y = -1.333333333z Simplifying y = -1.333333333zSubproblem 2
Set the factor '(3y + 4z)' equal to zero and attempt to solve: Simplifying 3y + 4z = 0 Solving 3y + 4z = 0 Move all terms containing y to the left, all other terms to the right. Add '-4z' to each side of the equation. 3y + 4z + -4z = 0 + -4z Combine like terms: 4z + -4z = 0 3y + 0 = 0 + -4z 3y = 0 + -4z Remove the zero: 3y = -4z Divide each side by '3'. y = -1.333333333z Simplifying y = -1.333333333zSolution
y = {-1.333333333z, -1.333333333z}
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