Z(2z-9)(z+3)=0

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Solution for Z(2z-9)(z+3)=0 equation:


Simplifying
Z(2z + -9)(z + 3) = 0

Reorder the terms:
Z(-9 + 2z)(z + 3) = 0

Reorder the terms:
Z(-9 + 2z)(3 + z) = 0

Multiply (-9 + 2z) * (3 + z)
Z(-9(3 + z) + 2z * (3 + z)) = 0
Z((3 * -9 + z * -9) + 2z * (3 + z)) = 0
Z((-27 + -9z) + 2z * (3 + z)) = 0
Z(-27 + -9z + (3 * 2z + z * 2z)) = 0
Z(-27 + -9z + (6z + 2z2)) = 0

Combine like terms: -9z + 6z = -3z
Z(-27 + -3z + 2z2) = 0
(-27 * Z + -3z * Z + 2z2 * Z) = 0
(-27Z + -3zZ + 2z2Z) = 0

Solving
-27Z + -3zZ + 2z2Z = 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(-27 + -3z + 2z2) = 0

Factor a trinomial.
Z((-3 + -1z)(9 + -2z)) = 0

Subproblem 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 = 0

Subproblem 2

Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 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 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Add 'z' to each side of the equation. -1z + z = 3 + z Combine like terms: -1z + z = 0 0 = 3 + z Simplifying 0 = 3 + 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 '(9 + -2z)' equal to zero and attempt to solve: Simplifying 9 + -2z = 0 Solving 9 + -2z = 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 + -2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2z = 0 + -9 -2z = 0 + -9 Combine like terms: 0 + -9 = -9 -2z = -9 Add '2z' to each side of the equation. -2z + 2z = -9 + 2z Combine like terms: -2z + 2z = 0 0 = -9 + 2z Simplifying 0 = -9 + 2z 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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