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

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

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

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

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

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

Combine like terms: -9z + -1z = -10z
(9 + -10z + z2) = 0

Solving
9 + -10z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
9 + -1z = 0

Solving
9 + -1z = 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 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {1, 9}