(5z+3)(8+z)=0

Solution for (5z+3)(8+z)=0 equation:

Simplifying
(5z + 3)(8 + z) = 0

Reorder the terms:
(3 + 5z)(8 + z) = 0

Multiply (3 + 5z) * (8 + z)
(3(8 + z) + 5z * (8 + z)) = 0
((8 * 3 + z * 3) + 5z * (8 + z)) = 0
((24 + 3z) + 5z * (8 + z)) = 0
(24 + 3z + (8 * 5z + z * 5z)) = 0
(24 + 3z + (40z + 5z2)) = 0

Combine like terms: 3z + 40z = 43z
(24 + 43z + 5z2) = 0

Solving
24 + 43z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(3 + 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 '(3 + 5z)' equal to zero and attempt to solve:

Simplifying
3 + 5z = 0

Solving
3 + 5z = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5z = 0 + -3
5z = 0 + -3

Combine like terms: 0 + -3 = -3
5z = -3

Divide each side by '5'.
z = -0.6

Simplifying
z = -0.6
Solution
z = {-8, -0.6}