(3+z)(5z+1)=0

Solution for (3+z)(5z+1)=0 equation:

Simplifying
(3 + z)(5z + 1) = 0

Reorder the terms:
(3 + z)(1 + 5z) = 0

Multiply (3 + z) * (1 + 5z)
(3(1 + 5z) + z(1 + 5z)) = 0
((1 * 3 + 5z * 3) + z(1 + 5z)) = 0
((3 + 15z) + z(1 + 5z)) = 0
(3 + 15z + (1 * z + 5z * z)) = 0
(3 + 15z + (1z + 5z2)) = 0

Combine like terms: 15z + 1z = 16z
(3 + 16z + 5z2) = 0

Solving
3 + 16z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(1 + 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 '(1 + 5z)' equal to zero and attempt to solve:

Simplifying
1 + 5z = 0

Solving
1 + 5z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5z = 0 + -1
5z = 0 + -1

Combine like terms: 0 + -1 = -1
5z = -1

Divide each side by '5'.
z = -0.2

Simplifying
z = -0.2
Solution
z = {-3, -0.2}