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

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

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

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

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

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

Combine like terms: -9z + 5z = -4z
-2z(-45 + -4z + z2) = 0
(-45 * -2z + -4z * -2z + z2 * -2z) = 0
(90z + 8z2 + -2z3) = 0

Solving
90z + 8z2 + -2z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(45 + 4z + -1z2) = 0

Factor a trinomial.
2z((9 + -1z)(5 + z)) = 0

Ignore the factor 2.
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 '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 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 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Subproblem 3
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {0, 9, -5}