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Simplifying (3y + -5z)(y + z) = 0 Multiply (3y + -5z) * (y + z) (3y * (y + z) + -5z * (y + z)) = 0 ((y * 3y + z * 3y) + -5z * (y + z)) = 0 Reorder the terms: ((3yz + 3y2) + -5z * (y + z)) = 0 ((3yz + 3y2) + -5z * (y + z)) = 0 (3yz + 3y2 + (y * -5z + z * -5z)) = 0 (3yz + 3y2 + (-5yz + -5z2)) = 0 Reorder the terms: (3yz + -5yz + 3y2 + -5z2) = 0 Combine like terms: 3yz + -5yz = -2yz (-2yz + 3y2 + -5z2) = 0 Solving -2yz + 3y2 + -5z2 = 0 Solving for variable 'y'. Factor a trinomial. (3y + -5z)(y + z) = 0Subproblem 1
Set the factor '(3y + -5z)' equal to zero and attempt to solve: Simplifying 3y + -5z = 0 Solving 3y + -5z = 0 Move all terms containing y to the left, all other terms to the right. Add '5z' to each side of the equation. 3y + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 3y + 0 = 0 + 5z 3y = 0 + 5z Remove the zero: 3y = 5z Divide each side by '3'. y = 1.666666667z Simplifying y = 1.666666667zSubproblem 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 = {1.666666667z, -1z}
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