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

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

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

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

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

Combine like terms: -2z + 9z = 7z
(-6 + 7z + 3z2) = 0

Solving
-6 + 7z + 3z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
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 = {-3, 0.6666666667}