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Simplifying Z6 = 81Z2 Solving Z6 = 81Z2 Solving for variable 'Z'. Reorder the terms: -81Z2 + Z6 = 81Z2 + -81Z2 Combine like terms: 81Z2 + -81Z2 = 0 -81Z2 + Z6 = 0 Factor out the Greatest Common Factor (GCF), 'Z2'. Z2(-81 + Z4) = 0 Factor a difference between two squares. Z2((9 + Z2)(-9 + Z2)) = 0 Factor a difference between two squares. Z2((9 + Z2)((3 + Z)(-3 + Z))) = 0Subproblem 1
Set the factor 'Z2' equal to zero and attempt to solve: Simplifying Z2 = 0 Solving Z2 = 0 Move all terms containing Z to the left, all other terms to the right. Simplifying Z2 = 0 Take the square root of each side: Z = {0}Subproblem 2
Set the factor '(9 + Z2)' equal to zero and attempt to solve: Simplifying 9 + Z2 = 0 Solving 9 + Z2 = 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 + Z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + Z2 = 0 + -9 Z2 = 0 + -9 Combine like terms: 0 + -9 = -9 Z2 = -9 Simplifying Z2 = -9 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + Z)' equal to zero and attempt to solve: Simplifying 3 + Z = 0 Solving 3 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + Z = 0 + -3 Z = 0 + -3 Combine like terms: 0 + -3 = -3 Z = -3 Simplifying Z = -3Subproblem 4
Set the factor '(-3 + Z)' equal to zero and attempt to solve: Simplifying -3 + Z = 0 Solving -3 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + Z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + Z = 0 + 3 Z = 0 + 3 Combine like terms: 0 + 3 = 3 Z = 3 Simplifying Z = 3Solution
Z = {0, -3, 3}
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