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

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


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

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

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