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Simplifying (Z2 + -36)(Z2 + -81) = 0 Reorder the terms: (-36 + Z2)(Z2 + -81) = 0 Reorder the terms: (-36 + Z2)(-81 + Z2) = 0 Multiply (-36 + Z2) * (-81 + Z2) (-36(-81 + Z2) + Z2(-81 + Z2)) = 0 ((-81 * -36 + Z2 * -36) + Z2(-81 + Z2)) = 0 ((2916 + -36Z2) + Z2(-81 + Z2)) = 0 (2916 + -36Z2 + (-81 * Z2 + Z2 * Z2)) = 0 (2916 + -36Z2 + (-81Z2 + Z4)) = 0 Combine like terms: -36Z2 + -81Z2 = -117Z2 (2916 + -117Z2 + Z4) = 0 Solving 2916 + -117Z2 + Z4 = 0 Solving for variable 'Z'. Factor a trinomial. (36 + -1Z2)(81 + -1Z2) = 0 Factor a difference between two squares. ((6 + Z)(6 + -1Z))(81 + -1Z2) = 0 Factor a difference between two squares. ((9 + Z)(9 + -1Z))(6 + Z)(6 + -1Z) = 0Subproblem 1
Set the factor '(6 + Z)' equal to zero and attempt to solve: Simplifying 6 + Z = 0 Solving 6 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + Z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + Z = 0 + -6 Z = 0 + -6 Combine like terms: 0 + -6 = -6 Z = -6 Simplifying Z = -6Subproblem 2
Set the factor '(6 + -1Z)' equal to zero and attempt to solve: Simplifying 6 + -1Z = 0 Solving 6 + -1Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1Z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1Z = 0 + -6 -1Z = 0 + -6 Combine like terms: 0 + -6 = -6 -1Z = -6 Divide each side by '-1'. Z = 6 Simplifying Z = 6Subproblem 3
Set the factor '(9 + Z)' equal to zero and attempt to solve: Simplifying 9 + Z = 0 Solving 9 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + Z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + Z = 0 + -9 Z = 0 + -9 Combine like terms: 0 + -9 = -9 Z = -9 Simplifying Z = -9Subproblem 4
Set the factor '(9 + -1Z)' equal to zero and attempt to solve: Simplifying 9 + -1Z = 0 Solving 9 + -1Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1Z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1Z = 0 + -9 -1Z = 0 + -9 Combine like terms: 0 + -9 = -9 -1Z = -9 Divide each side by '-1'. Z = 9 Simplifying Z = 9Solution
Z = {-6, 6, -9, 9}
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