3z^2=2z^3

Solution for 3z^2=2z^3 equation:

Simplifying
3z2 = 2z3

Solving
3z2 = 2z3

Solving for variable 'z'.

Combine like terms: 2z3 + -2z3 = 0
3z2 + -2z3 = 0

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(3 + -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 '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {0, 1.5}