(3z+8)(4-z)=0

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Solution for (3z+8)(4-z)=0 equation: 


Simplifying
(3z + 8)(4 + -1z) = 0

Reorder the terms:
(8 + 3z)(4 + -1z) = 0

Multiply (8 + 3z) * (4 + -1z)
(8(4 + -1z) + 3z * (4 + -1z)) = 0
((4 * 8 + -1z * 8) + 3z * (4 + -1z)) = 0
((32 + -8z) + 3z * (4 + -1z)) = 0
(32 + -8z + (4 * 3z + -1z * 3z)) = 0
(32 + -8z + (12z + -3z2)) = 0

Combine like terms: -8z + 12z = 4z
(32 + 4z + -3z2) = 0

Solving
32 + 4z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + -1z)(8 + 3z) = 0


Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4

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 = {4, -2.666666667}

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