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

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

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

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

Multiply (8 + 3z) * (3 + z)
(8(3 + z) + 3z * (3 + z)) = 0
((3 * 8 + z * 8) + 3z * (3 + z)) = 0
((24 + 8z) + 3z * (3 + z)) = 0
(24 + 8z + (3 * 3z + z * 3z)) = 0
(24 + 8z + (9z + 3z2)) = 0

Combine like terms: 8z + 9z = 17z
(24 + 17z + 3z2) = 0

Solving
24 + 17z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(8 + 3z) = 0

Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve:

Simplifying
8 + 3z = 0

Solving
8 + 3z = 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 + 3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3z = 0 + -8
3z = 0 + -8

Combine like terms: 0 + -8 = -8
3z = -8

Divide each side by '3'.
z = -2.666666667

Simplifying
z = -2.666666667
Solution
z = {-3, -2.666666667}