2z^2(z-2)=0

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

Simplifying
2z2(z + -2) = 0

Reorder the terms:
2z2(-2 + z) = 0
(-2 * 2z2 + z * 2z2) = 0
(-4z2 + 2z3) = 0

Solving
-4z2 + 2z3 = 0

Solving for variable 'z'.

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

Ignore the factor 2.
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 '(-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, 2}