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

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

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

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

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

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

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

Solving
-6 + -3z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1z + z2) = 0

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

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

Simplifying
-1 + -1z = 0

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

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

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

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

Simplifying
z = -1
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-1, 2}