(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 = 7z
(72 + 7z + -2z2) = 0

Solving
72 + 7z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z)(9 + 2z) = 0


Subproblem 1
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 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 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
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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