-5z(z-1)(z+2)=0

Solution for -5z(z-1)(z+2)=0 equation:

Simplifying
-5z(z + -1)(z + 2) = 0

Reorder the terms:
-5z(-1 + z)(z + 2) = 0

Reorder the terms:
-5z(-1 + z)(2 + z) = 0

Multiply (-1 + z) * (2 + z)
-5z(-1(2 + z) + z(2 + z)) = 0
-5z((2 * -1 + z * -1) + z(2 + z)) = 0
-5z((-2 + -1z) + z(2 + z)) = 0
-5z(-2 + -1z + (2 * z + z * z)) = 0
-5z(-2 + -1z + (2z + z2)) = 0

Combine like terms: -1z + 2z = 1z
-5z(-2 + 1z + z2) = 0
(-2 * -5z + 1z * -5z + z2 * -5z) = 0
(10z + -5z2 + -5z3) = 0

Solving
10z + -5z2 + -5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(2 + -1z + -1z2) = 0

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

Ignore the factor 5.
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 '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Subproblem 3
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 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 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

Simplifying
z = -2
Solution
z = {0, 1, -2}