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Simplifying (2z + y)(3z + y) = 0 Reorder the terms: (y + 2z)(3z + y) = 0 Reorder the terms: (y + 2z)(y + 3z) = 0 Multiply (y + 2z) * (y + 3z) (y(y + 3z) + 2z * (y + 3z)) = 0 ((y * y + 3z * y) + 2z * (y + 3z)) = 0 Reorder the terms: ((3yz + y2) + 2z * (y + 3z)) = 0 ((3yz + y2) + 2z * (y + 3z)) = 0 (3yz + y2 + (y * 2z + 3z * 2z)) = 0 (3yz + y2 + (2yz + 6z2)) = 0 Reorder the terms: (3yz + 2yz + y2 + 6z2) = 0 Combine like terms: 3yz + 2yz = 5yz (5yz + y2 + 6z2) = 0 Solving 5yz + y2 + 6z2 = 0 Solving for variable 'y'. Factor a trinomial. (y + 2z)(y + 3z) = 0Subproblem 1
Set the factor '(y + 2z)' equal to zero and attempt to solve: Simplifying y + 2z = 0 Solving y + 2z = 0 Move all terms containing y to the left, all other terms to the right. Add '-2z' to each side of the equation. y + 2z + -2z = 0 + -2z Combine like terms: 2z + -2z = 0 y + 0 = 0 + -2z y = 0 + -2z Remove the zero: y = -2z Simplifying y = -2zSubproblem 2
Set the factor '(y + 3z)' equal to zero and attempt to solve: Simplifying y + 3z = 0 Solving y + 3z = 0 Move all terms containing y to the left, all other terms to the right. Add '-3z' to each side of the equation. y + 3z + -3z = 0 + -3z Combine like terms: 3z + -3z = 0 y + 0 = 0 + -3z y = 0 + -3z Remove the zero: y = -3z Simplifying y = -3zSolution
y = {-2z, -3z}
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