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

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

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

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

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

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

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

Solving
-2z + 1z2 + z3 = 0

Solving for variable 'z'.

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

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

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 3
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
Solution
z = {0, -2, 1}