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

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

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

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

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

Combine like terms: 9z + 5z = 14z
(15 + 14z + 3z2) = 0

Solving
15 + 14z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(5 + 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 '(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 = {-3, -1.666666667}