(8+z)(5z+7)=0

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Solution for (8+z)(5z+7)=0 equation: 


Simplifying
(8 + z)(5z + 7) = 0

Reorder the terms:
(8 + z)(7 + 5z) = 0

Multiply (8 + z) * (7 + 5z)
(8(7 + 5z) + z(7 + 5z)) = 0
((7 * 8 + 5z * 8) + z(7 + 5z)) = 0
((56 + 40z) + z(7 + 5z)) = 0
(56 + 40z + (7 * z + 5z * z)) = 0
(56 + 40z + (7z + 5z2)) = 0

Combine like terms: 40z + 7z = 47z
(56 + 47z + 5z2) = 0

Solving
56 + 47z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(7 + 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 '(7 + 5z)' equal to zero and attempt to solve:

Simplifying
7 + 5z = 0

Solving
7 + 5z = 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 + 5z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5z = 0 + -7
5z = 0 + -7

Combine like terms: 0 + -7 = -7
5z = -7

Divide each side by '5'.
z = -1.4

Simplifying
z = -1.4
Solution
z = {-8, -1.4}

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