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

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


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

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

Multiply (-8 + 3z) * (5 + -1z)
(-8(5 + -1z) + 3z * (5 + -1z)) = 0
((5 * -8 + -1z * -8) + 3z * (5 + -1z)) = 0
((-40 + 8z) + 3z * (5 + -1z)) = 0
(-40 + 8z + (5 * 3z + -1z * 3z)) = 0
(-40 + 8z + (15z + -3z2)) = 0

Combine like terms: 8z + 15z = 23z
(-40 + 23z + -3z2) = 0

Solving
-40 + 23z + -3z2 = 0

Solving for variable 'z'.

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


Subproblem 1
Set the factor '(-5 + z)' equal to zero and attempt to solve:

Simplifying
-5 + z = 0

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

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

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

Simplifying
z = 5

Subproblem 2
Set the factor '(8 + -3z)' equal to zero and attempt to solve:

Simplifying
8 + -3z = 0

Solving
8 + -3z = 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 + -3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3z = 0 + -8
-3z = 0 + -8

Combine like terms: 0 + -8 = -8
-3z = -8

Divide each side by '-3'.
z = 2.666666667

Simplifying
z = 2.666666667
Solution
z = {5, 2.666666667}

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