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

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


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

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

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

Combine like terms: 7z + 16z = 23z
(56 + 23z + 2z2) = 0

Solving
56 + 23z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(7 + 2z) = 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 '(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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