(3z-2)(1-z)=0

Solution for (3z-2)(1-z)=0 equation:

Simplifying
(3z + -2)(1 + -1z) = 0

Reorder the terms:
(-2 + 3z)(1 + -1z) = 0

Multiply (-2 + 3z) * (1 + -1z)
(-2(1 + -1z) + 3z * (1 + -1z)) = 0
((1 * -2 + -1z * -2) + 3z * (1 + -1z)) = 0
((-2 + 2z) + 3z * (1 + -1z)) = 0
(-2 + 2z + (1 * 3z + -1z * 3z)) = 0
(-2 + 2z + (3z + -3z2)) = 0

Combine like terms: 2z + 3z = 5z
(-2 + 5z + -3z2) = 0

Solving
-2 + 5z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + z)(2 + -3z) = 0

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

Simplifying
-1 + z = 0

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

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

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

Simplifying
z = 1
Subproblem 2
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
Solution
z = {1, 0.6666666667}