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

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


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

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

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

Combine like terms: 9z + 16z = 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}

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