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

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

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

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

Multiply (3 + 2z) * (2 + -1z)
(3(2 + -1z) + 2z * (2 + -1z)) = 0
((2 * 3 + -1z * 3) + 2z * (2 + -1z)) = 0
((6 + -3z) + 2z * (2 + -1z)) = 0
(6 + -3z + (2 * 2z + -1z * 2z)) = 0
(6 + -3z + (4z + -2z2)) = 0

Combine like terms: -3z + 4z = 1z
(6 + 1z + -2z2) = 0

Solving
6 + 1z + -2z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
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 = {2, -1.5}