(8-z)(2z+7)=0

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Solution for (8-z)(2z+7)=0 equation: 


Simplifying
(8 + -1z)(2z + 7) = 0

Reorder the terms:
(8 + -1z)(7 + 2z) = 0

Multiply (8 + -1z) * (7 + 2z)
(8(7 + 2z) + -1z * (7 + 2z)) = 0
((7 * 8 + 2z * 8) + -1z * (7 + 2z)) = 0
((56 + 16z) + -1z * (7 + 2z)) = 0
(56 + 16z + (7 * -1z + 2z * -1z)) = 0
(56 + 16z + (-7z + -2z2)) = 0

Combine like terms: 16z + -7z = 9z
(56 + 9z + -2z2) = 0

Solving
56 + 9z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z)(7 + 2z) = 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 + 2z)' equal to zero and attempt to solve:

Simplifying
7 + 2z = 0

Solving
7 + 2z = 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 + 2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2z = 0 + -7
2z = 0 + -7

Combine like terms: 0 + -7 = -7
2z = -7

Divide each side by '2'.
z = -3.5

Simplifying
z = -3.5
Solution
z = {8, -3.5}

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