(8-z)(2z+5)=0

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Solution for (8-z)(2z+5)=0 equation: 


Simplifying
(8 + -1z)(2z + 5) = 0

Reorder the terms:
(8 + -1z)(5 + 2z) = 0

Multiply (8 + -1z) * (5 + 2z)
(8(5 + 2z) + -1z * (5 + 2z)) = 0
((5 * 8 + 2z * 8) + -1z * (5 + 2z)) = 0
((40 + 16z) + -1z * (5 + 2z)) = 0
(40 + 16z + (5 * -1z + 2z * -1z)) = 0
(40 + 16z + (-5z + -2z2)) = 0

Combine like terms: 16z + -5z = 11z
(40 + 11z + -2z2) = 0

Solving
40 + 11z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z)(5 + 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 '(5 + 2z)' equal to zero and attempt to solve:

Simplifying
5 + 2z = 0

Solving
5 + 2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 2z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2z = 0 + -5
2z = 0 + -5

Combine like terms: 0 + -5 = -5
2z = -5

Divide each side by '2'.
z = -2.5

Simplifying
z = -2.5
Solution
z = {8, -2.5}

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