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

Solution for (9-z)(2z-3)=0 equation:

Simplifying
(9 + -1z)(2z + -3) = 0

Reorder the terms:
(9 + -1z)(-3 + 2z) = 0

Multiply (9 + -1z) * (-3 + 2z)
(9(-3 + 2z) + -1z * (-3 + 2z)) = 0
((-3 * 9 + 2z * 9) + -1z * (-3 + 2z)) = 0
((-27 + 18z) + -1z * (-3 + 2z)) = 0
(-27 + 18z + (-3 * -1z + 2z * -1z)) = 0
(-27 + 18z + (3z + -2z2)) = 0

Combine like terms: 18z + 3z = 21z
(-27 + 21z + -2z2) = 0

Solving
-27 + 21z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + z)(3 + -2z) = 0

Subproblem 1
Set the factor '(-9 + z)' equal to zero and attempt to solve:

Simplifying
-9 + z = 0

Solving
-9 + z = 0

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

Add '9' to each side of the equation.
-9 + 9 + z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + z = 0 + 9
z = 0 + 9

Combine like terms: 0 + 9 = 9
z = 9

Simplifying
z = 9
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 = {9, 1.5}