(5z+9)(3+z)=0

Solution for (5z+9)(3+z)=0 equation:

Simplifying
(5z + 9)(3 + z) = 0

Reorder the terms:
(9 + 5z)(3 + z) = 0

Multiply (9 + 5z) * (3 + z)
(9(3 + z) + 5z * (3 + z)) = 0
((3 * 9 + z * 9) + 5z * (3 + z)) = 0
((27 + 9z) + 5z * (3 + z)) = 0
(27 + 9z + (3 * 5z + z * 5z)) = 0
(27 + 9z + (15z + 5z2)) = 0

Combine like terms: 9z + 15z = 24z
(27 + 24z + 5z2) = 0

Solving
27 + 24z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(9 + 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 '(9 + 5z)' equal to zero and attempt to solve:

Simplifying
9 + 5z = 0

Solving
9 + 5z = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5z = 0 + -9
5z = 0 + -9

Combine like terms: 0 + -9 = -9
5z = -9

Divide each side by '5'.
z = -1.8

Simplifying
z = -1.8
Solution
z = {-3, -1.8}