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

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


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

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

Multiply (8 + 5z) * (2 + -1z)
(8(2 + -1z) + 5z * (2 + -1z)) = 0
((2 * 8 + -1z * 8) + 5z * (2 + -1z)) = 0
((16 + -8z) + 5z * (2 + -1z)) = 0
(16 + -8z + (2 * 5z + -1z * 5z)) = 0
(16 + -8z + (10z + -5z2)) = 0

Combine like terms: -8z + 10z = 2z
(16 + 2z + -5z2) = 0

Solving
16 + 2z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z)(8 + 5z) = 0


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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2

Subproblem 2
Set the factor '(8 + 5z)' equal to zero and attempt to solve:

Simplifying
8 + 5z = 0

Solving
8 + 5z = 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 + 5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5z = 0 + -8
5z = 0 + -8

Combine like terms: 0 + -8 = -8
5z = -8

Divide each side by '5'.
z = -1.6

Simplifying
z = -1.6
Solution
z = {2, -1.6}

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