(2Z-3)*(3Z-2)=0

Solution for (2Z-3)*(3Z-2)=0 equation:

Simplifying
(2Z + -3)(3Z + -2) = 0

Reorder the terms:
(-3 + 2Z)(3Z + -2) = 0

Reorder the terms:
(-3 + 2Z)(-2 + 3Z) = 0

Multiply (-3 + 2Z) * (-2 + 3Z)
(-3(-2 + 3Z) + 2Z * (-2 + 3Z)) = 0
((-2 * -3 + 3Z * -3) + 2Z * (-2 + 3Z)) = 0
((6 + -9Z) + 2Z * (-2 + 3Z)) = 0
(6 + -9Z + (-2 * 2Z + 3Z * 2Z)) = 0
(6 + -9Z + (-4Z + 6Z2)) = 0

Combine like terms: -9Z + -4Z = -13Z
(6 + -13Z + 6Z2) = 0

Solving
6 + -13Z + 6Z2 = 0

Solving for variable 'Z'.

Factor a trinomial.
(2 + -3Z)(3 + -2Z) = 0

Subproblem 1
Set the factor '(2 + -3Z)' equal to zero and attempt to solve:

Simplifying
2 + -3Z = 0

Solving
2 + -3Z = 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 + -3Z = 0 + -2

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

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

Divide each side by '-3'.
Z = 0.6666666667

Simplifying
Z = 0.6666666667
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 = {0.6666666667, 1.5}