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

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


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

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

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

Multiply (-9 + 2z) * (2 + z)
Z(-9(2 + z) + 2z * (2 + z)) = 0
Z((2 * -9 + z * -9) + 2z * (2 + z)) = 0
Z((-18 + -9z) + 2z * (2 + z)) = 0
Z(-18 + -9z + (2 * 2z + z * 2z)) = 0
Z(-18 + -9z + (4z + 2z2)) = 0

Combine like terms: -9z + 4z = -5z
Z(-18 + -5z + 2z2) = 0
(-18 * Z + -5z * Z + 2z2 * Z) = 0
(-18Z + -5zZ + 2z2Z) = 0

Solving
-18Z + -5zZ + 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(-18 + -5z + 2z2) = 0

Factor a trinomial.
Z((-2 + -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 '(-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 '(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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