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

Solution for (8-z)(2z-9)=0 equation:

Simplifying
(8 + -1z)(2z + -9) = 0

Reorder the terms:
(8 + -1z)(-9 + 2z) = 0

Multiply (8 + -1z) * (-9 + 2z)
(8(-9 + 2z) + -1z * (-9 + 2z)) = 0
((-9 * 8 + 2z * 8) + -1z * (-9 + 2z)) = 0
((-72 + 16z) + -1z * (-9 + 2z)) = 0
(-72 + 16z + (-9 * -1z + 2z * -1z)) = 0
(-72 + 16z + (9z + -2z2)) = 0

Combine like terms: 16z + 9z = 25z
(-72 + 25z + -2z2) = 0

Solving
-72 + 25z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(9 + -2z) = 0

Subproblem 1
Set the factor '(-8 + z)' equal to zero and attempt to solve:

Simplifying
-8 + z = 0

Solving
-8 + z = 0

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

Add '8' to each side of the equation.
-8 + 8 + z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + z = 0 + 8
z = 0 + 8

Combine like terms: 0 + 8 = 8
z = 8

Simplifying
z = 8
Subproblem 2
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
Solution
z = {8, 4.5}