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Simplifying Z(4z + -7)(z + 5) = 0 Reorder the terms: Z(-7 + 4z)(z + 5) = 0 Reorder the terms: Z(-7 + 4z)(5 + z) = 0 Multiply (-7 + 4z) * (5 + z) Z(-7(5 + z) + 4z * (5 + z)) = 0 Z((5 * -7 + z * -7) + 4z * (5 + z)) = 0 Z((-35 + -7z) + 4z * (5 + z)) = 0 Z(-35 + -7z + (5 * 4z + z * 4z)) = 0 Z(-35 + -7z + (20z + 4z2)) = 0 Combine like terms: -7z + 20z = 13z Z(-35 + 13z + 4z2) = 0 (-35 * Z + 13z * Z + 4z2 * Z) = 0 (-35Z + 13zZ + 4z2Z) = 0 Solving -35Z + 13zZ + 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(-35 + 13z + 4z2) = 0 Factor a trinomial. Z((-5 + -1z)(7 + -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 '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 0 Move all terms containing Z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Add 'z' to each side of the equation. -1z + z = 5 + z Combine like terms: -1z + z = 0 0 = 5 + z Simplifying 0 = 5 + 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 '(7 + -4z)' equal to zero and attempt to solve: Simplifying 7 + -4z = 0 Solving 7 + -4z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4z = 0 + -7 -4z = 0 + -7 Combine like terms: 0 + -7 = -7 -4z = -7 Add '4z' to each side of the equation. -4z + 4z = -7 + 4z Combine like terms: -4z + 4z = 0 0 = -7 + 4z Simplifying 0 = -7 + 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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