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

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

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

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

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

Combine like terms: 12z + -3z = 9z
(18 + 9z + -2z2) = 0

Solving
18 + 9z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(3 + 2z) = 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 '(3 + 2z)' equal to zero and attempt to solve:

Simplifying
3 + 2z = 0

Solving
3 + 2z = 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 + 2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {6, -1.5}