(3z+5)(6+z)=0

Solution for (3z+5)(6+z)=0 equation:

Simplifying
(3z + 5)(6 + z) = 0

Reorder the terms:
(5 + 3z)(6 + z) = 0

Multiply (5 + 3z) * (6 + z)
(5(6 + z) + 3z * (6 + z)) = 0
((6 * 5 + z * 5) + 3z * (6 + z)) = 0
((30 + 5z) + 3z * (6 + z)) = 0
(30 + 5z + (6 * 3z + z * 3z)) = 0
(30 + 5z + (18z + 3z2)) = 0

Combine like terms: 5z + 18z = 23z
(30 + 23z + 3z2) = 0

Solving
30 + 23z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + z)(5 + 3z) = 0

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(5 + 3z)' equal to zero and attempt to solve:

Simplifying
5 + 3z = 0

Solving
5 + 3z = 0

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

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

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

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

Divide each side by '3'.
z = -1.666666667

Simplifying
z = -1.666666667
Solution
z = {-6, -1.666666667}