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

Solution for (6-z)(3z+2)=0 equation:

Simplifying
(6 + -1z)(3z + 2) = 0

Reorder the terms:
(6 + -1z)(2 + 3z) = 0

Multiply (6 + -1z) * (2 + 3z)
(6(2 + 3z) + -1z * (2 + 3z)) = 0
((2 * 6 + 3z * 6) + -1z * (2 + 3z)) = 0
((12 + 18z) + -1z * (2 + 3z)) = 0
(12 + 18z + (2 * -1z + 3z * -1z)) = 0
(12 + 18z + (-2z + -3z2)) = 0

Combine like terms: 18z + -2z = 16z
(12 + 16z + -3z2) = 0

Solving
12 + 16z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(2 + 3z) = 0

Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
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 = {6, -0.6666666667}