(5z-4)(8-z)=0

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Solution for (5z-4)(8-z)=0 equation: 


Simplifying
(5z + -4)(8 + -1z) = 0

Reorder the terms:
(-4 + 5z)(8 + -1z) = 0

Multiply (-4 + 5z) * (8 + -1z)
(-4(8 + -1z) + 5z * (8 + -1z)) = 0
((8 * -4 + -1z * -4) + 5z * (8 + -1z)) = 0
((-32 + 4z) + 5z * (8 + -1z)) = 0
(-32 + 4z + (8 * 5z + -1z * 5z)) = 0
(-32 + 4z + (40z + -5z2)) = 0

Combine like terms: 4z + 40z = 44z
(-32 + 44z + -5z2) = 0

Solving
-32 + 44z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(4 + -5z) = 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 '(4 + -5z)' equal to zero and attempt to solve:

Simplifying
4 + -5z = 0

Solving
4 + -5z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5z = 0 + -4
-5z = 0 + -4

Combine like terms: 0 + -4 = -4
-5z = -4

Divide each side by '-5'.
z = 0.8

Simplifying
z = 0.8
Solution
z = {8, 0.8}

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