z(2z-9)(z+5)=0

Solution for z(2z-9)(z+5)=0 equation:

Simplifying
z(2z + -9)(z + 5) = 0

Reorder the terms:
z(-9 + 2z)(z + 5) = 0

Reorder the terms:
z(-9 + 2z)(5 + z) = 0

Multiply (-9 + 2z) * (5 + z)
z(-9(5 + z) + 2z * (5 + z)) = 0
z((5 * -9 + z * -9) + 2z * (5 + z)) = 0
z((-45 + -9z) + 2z * (5 + z)) = 0
z(-45 + -9z + (5 * 2z + z * 2z)) = 0
z(-45 + -9z + (10z + 2z2)) = 0

Combine like terms: -9z + 10z = 1z
z(-45 + 1z + 2z2) = 0
(-45 * z + 1z * z + 2z2 * z) = 0
(-45z + 1z2 + 2z3) = 0

Solving
-45z + 1z2 + 2z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-45 + z + 2z2) = 0

Factor a trinomial.
z((-5 + -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 '(-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

Divide each side by '-1'.
z = -5

Simplifying
z = -5
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

Divide each side by '-2'.
z = 4.5

Simplifying
z = 4.5
Solution
z = {0, -5, 4.5}