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

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

Simplifying
(z2)(2z + -1) = 0

Reorder the terms:
z2(-1 + 2z) = 0
(-1 * z2 + 2z * z2) = 0
(-1z2 + 2z3) = 0

Solving
-1z2 + 2z3 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-1 + 2z)' equal to zero and attempt to solve:

Simplifying
-1 + 2z = 0

Solving
-1 + 2z = 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 + 2z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2z = 0 + 1
2z = 0 + 1

Combine like terms: 0 + 1 = 1
2z = 1

Divide each side by '2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0, 0.5}