(2z-9)(4-z)=0

Solution for (2z-9)(4-z)=0 equation:

Simplifying
(2z + -9)(4 + -1z) = 0

Reorder the terms:
(-9 + 2z)(4 + -1z) = 0

Multiply (-9 + 2z) * (4 + -1z)
(-9(4 + -1z) + 2z * (4 + -1z)) = 0
((4 * -9 + -1z * -9) + 2z * (4 + -1z)) = 0
((-36 + 9z) + 2z * (4 + -1z)) = 0
(-36 + 9z + (4 * 2z + -1z * 2z)) = 0
(-36 + 9z + (8z + -2z2)) = 0

Combine like terms: 9z + 8z = 17z
(-36 + 17z + -2z2) = 0

Solving
-36 + 17z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + 2z)(4 + -1z) = 0

Subproblem 1
Set the factor '(-9 + 2z)' equal to zero and attempt to solve:

Simplifying
-9 + 2z = 0

Solving
-9 + 2z = 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 + 2z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2z = 0 + 9
2z = 0 + 9

Combine like terms: 0 + 9 = 9
2z = 9

Divide each side by '2'.
z = 4.5

Simplifying
z = 4.5
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {4.5, 4}