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

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

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

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

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

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

Combine like terms: 9z + -1z = 8z
-2(9 + 8z + -1z2) = 0
(9 * -2 + 8z * -2 + -1z2 * -2) = 0
(-18 + -16z + 2z2) = 0

Solving
-18 + -16z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -8z + z2) = 0

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

Ignore the factor 2.
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}