Z(6z-7)(z+5)=0

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Solution for Z(6z-7)(z+5)=0 equation: 


Simplifying
Z(6z + -7)(z + 5) = 0

Reorder the terms:
Z(-7 + 6z)(z + 5) = 0

Reorder the terms:
Z(-7 + 6z)(5 + z) = 0

Multiply (-7 + 6z) * (5 + z)
Z(-7(5 + z) + 6z * (5 + z)) = 0
Z((5 * -7 + z * -7) + 6z * (5 + z)) = 0
Z((-35 + -7z) + 6z * (5 + z)) = 0
Z(-35 + -7z + (5 * 6z + z * 6z)) = 0
Z(-35 + -7z + (30z + 6z2)) = 0

Combine like terms: -7z + 30z = 23z
Z(-35 + 23z + 6z2) = 0
(-35 * Z + 23z * Z + 6z2 * Z) = 0
(-35Z + 23zZ + 6z2Z) = 0

Solving
-35Z + 23zZ + 6z2Z = 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 + 23z + 6z2) = 0

Factor a trinomial.
Z((-5 + -1z)(7 + -6z)) = 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 '(-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 + -6z)' equal to zero and attempt to solve:

Simplifying
7 + -6z = 0

Solving
7 + -6z = 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 + -6z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6z = 0 + -7
-6z = 0 + -7

Combine like terms: 0 + -7 = -7
-6z = -7

Add '6z' to each side of the equation.
-6z + 6z = -7 + 6z

Combine like terms: -6z + 6z = 0
0 = -7 + 6z

Simplifying
0 = -7 + 6z

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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