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

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

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

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

Multiply (6 + 5z) * (3 + z)
(6(3 + z) + 5z * (3 + z)) = 0
((3 * 6 + z * 6) + 5z * (3 + z)) = 0
((18 + 6z) + 5z * (3 + z)) = 0
(18 + 6z + (3 * 5z + z * 5z)) = 0
(18 + 6z + (15z + 5z2)) = 0

Combine like terms: 6z + 15z = 21z
(18 + 21z + 5z2) = 0

Solving
18 + 21z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(6 + 5z) = 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 '(6 + 5z)' equal to zero and attempt to solve:

Simplifying
6 + 5z = 0

Solving
6 + 5z = 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 + 5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5z = 0 + -6
5z = 0 + -6

Combine like terms: 0 + -6 = -6
5z = -6

Divide each side by '5'.
z = -1.2

Simplifying
z = -1.2
Solution
z = {-3, -1.2}