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Simplifying Z(z + 1)(z + -2) = 0 Reorder the terms: Z(1 + z)(z + -2) = 0 Reorder the terms: Z(1 + z)(-2 + z) = 0 Multiply (1 + z) * (-2 + z) Z(1(-2 + z) + z(-2 + z)) = 0 Z((-2 * 1 + z * 1) + z(-2 + z)) = 0 Z((-2 + 1z) + z(-2 + z)) = 0 Z(-2 + 1z + (-2 * z + z * z)) = 0 Z(-2 + 1z + (-2z + z2)) = 0 Combine like terms: 1z + -2z = -1z Z(-2 + -1z + z2) = 0 (-2 * Z + -1z * Z + z2 * Z) = 0 (-2Z + -1zZ + z2Z) = 0 Solving -2Z + -1zZ + z2Z = 0 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'Z'. Z(-2 + -1z + z2) = 0 Factor a trinomial. Z((-1 + -1z)(2 + -1z)) = 0Subproblem 1
Set the factor 'Z' equal to zero and attempt to solve: Simplifying Z = 0 Solving Z = 0 Move all terms containing Z to the left, all other terms to the right. Simplifying Z = 0Subproblem 2
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing Z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Add 'z' to each side of the equation. -1z + z = 1 + z Combine like terms: -1z + z = 0 0 = 1 + z Simplifying 0 = 1 + z 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 '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Add 'z' to each side of the equation. -1z + z = -2 + z Combine like terms: -1z + z = 0 0 = -2 + z Simplifying 0 = -2 + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
Z = {0}
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