(2z-1)(9-z)=0

Solution for (2z-1)(9-z)=0 equation:

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

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

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

Combine like terms: 1z + 18z = 19z
(-9 + 19z + -2z2) = 0

Solving
-9 + 19z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + z)(1 + -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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {9, 0.5}