(3z+7)(8-z)=0

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Solution for (3z+7)(8-z)=0 equation: 


Simplifying
(3z + 7)(8 + -1z) = 0

Reorder the terms:
(7 + 3z)(8 + -1z) = 0

Multiply (7 + 3z) * (8 + -1z)
(7(8 + -1z) + 3z * (8 + -1z)) = 0
((8 * 7 + -1z * 7) + 3z * (8 + -1z)) = 0
((56 + -7z) + 3z * (8 + -1z)) = 0
(56 + -7z + (8 * 3z + -1z * 3z)) = 0
(56 + -7z + (24z + -3z2)) = 0

Combine like terms: -7z + 24z = 17z
(56 + 17z + -3z2) = 0

Solving
56 + 17z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z)(7 + 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 '(7 + 3z)' equal to zero and attempt to solve:

Simplifying
7 + 3z = 0

Solving
7 + 3z = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3z = 0 + -7
3z = 0 + -7

Combine like terms: 0 + -7 = -7
3z = -7

Divide each side by '3'.
z = -2.333333333

Simplifying
z = -2.333333333
Solution
z = {8, -2.333333333}

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