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

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

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

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

Multiply (-3 + Z) * (1 + -2Z)
3(-3(1 + -2Z) + Z(1 + -2Z)) = 0
3((1 * -3 + -2Z * -3) + Z(1 + -2Z)) = 0
3((-3 + 6Z) + Z(1 + -2Z)) = 0
3(-3 + 6Z + (1 * Z + -2Z * Z)) = 0
3(-3 + 6Z + (1Z + -2Z2)) = 0

Combine like terms: 6Z + 1Z = 7Z
3(-3 + 7Z + -2Z2) = 0
(-3 * 3 + 7Z * 3 + -2Z2 * 3) = 0
(-9 + 21Z + -6Z2) = 0

Solving
-9 + 21Z + -6Z2 = 0

Solving for variable 'Z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 7Z + -2Z2) = 0

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

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

Simplifying
-3 + Z = 0

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

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

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

Simplifying
Z = 3
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 = {3, 0.5}