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

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

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

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

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

Combine like terms: 2z + 9z = 11z
(-9 + 11z + -2z2) = 0

Solving
-9 + 11z + -2z2 = 0

Solving for variable 'z'.

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 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 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Solution
z = {4.5, 1}