(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 = 29z
(-40 + 29z + -3z2) = 0

Solving
-40 + 29z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(5 + -3z) = 0


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

Simplifying
-8 + z = 0

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

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

Combine like terms: 0 + 8 = 8
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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