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Simplifying Z(4z + -3)(z + 2) = 0 Reorder the terms: Z(-3 + 4z)(z + 2) = 0 Reorder the terms: Z(-3 + 4z)(2 + z) = 0 Multiply (-3 + 4z) * (2 + z) Z(-3(2 + z) + 4z * (2 + z)) = 0 Z((2 * -3 + z * -3) + 4z * (2 + z)) = 0 Z((-6 + -3z) + 4z * (2 + z)) = 0 Z(-6 + -3z + (2 * 4z + z * 4z)) = 0 Z(-6 + -3z + (8z + 4z2)) = 0 Combine like terms: -3z + 8z = 5z Z(-6 + 5z + 4z2) = 0 (-6 * Z + 5z * Z + 4z2 * Z) = 0 (-6Z + 5zZ + 4z2Z) = 0 Solving -6Z + 5zZ + 4z2Z = 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(-6 + 5z + 4z2) = 0 Factor a trinomial. Z((-2 + -1z)(3 + -4z)) = 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 '(-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.Subproblem 3
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Add '4z' to each side of the equation. -4z + 4z = -3 + 4z Combine like terms: -4z + 4z = 0 0 = -3 + 4z Simplifying 0 = -3 + 4z 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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