(3z-9)(2z+1)=0

Solution for (3z-9)(2z+1)=0 equation:

Simplifying
(3z + -9)(2z + 1) = 0

Reorder the terms:
(-9 + 3z)(2z + 1) = 0

Reorder the terms:
(-9 + 3z)(1 + 2z) = 0

Multiply (-9 + 3z) * (1 + 2z)
(-9(1 + 2z) + 3z * (1 + 2z)) = 0
((1 * -9 + 2z * -9) + 3z * (1 + 2z)) = 0
((-9 + -18z) + 3z * (1 + 2z)) = 0
(-9 + -18z + (1 * 3z + 2z * 3z)) = 0
(-9 + -18z + (3z + 6z2)) = 0

Combine like terms: -18z + 3z = -15z
(-9 + -15z + 6z2) = 0

Solving
-9 + -15z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -5z + 2z2) = 0

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

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

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-0.5, 3}