(3z+5)(8-z)=0

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Solution for (3z+5)(8-z)=0 equation: 


Simplifying
(3z + 5)(8 + -1z) = 0

Reorder the terms:
(5 + 3z)(8 + -1z) = 0

Multiply (5 + 3z) * (8 + -1z)
(5(8 + -1z) + 3z * (8 + -1z)) = 0
((8 * 5 + -1z * 5) + 3z * (8 + -1z)) = 0
((40 + -5z) + 3z * (8 + -1z)) = 0
(40 + -5z + (8 * 3z + -1z * 3z)) = 0
(40 + -5z + (24z + -3z2)) = 0

Combine like terms: -5z + 24z = 19z
(40 + 19z + -3z2) = 0

Solving
40 + 19z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z)(5 + 3z) = 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 + 3z)' equal to zero and attempt to solve:

Simplifying
5 + 3z = 0

Solving
5 + 3z = 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 + 3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3z = 0 + -5
3z = 0 + -5

Combine like terms: 0 + -5 = -5
3z = -5

Divide each side by '3'.
z = -1.666666667

Simplifying
z = -1.666666667
Solution
z = {8, -1.666666667}

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