(3+z)(2z+1)=0

Solution for (3+z)(2z+1)=0 equation:

Simplifying
(3 + z)(2z + 1) = 0

Reorder the terms:
(3 + z)(1 + 2z) = 0

Multiply (3 + z) * (1 + 2z)
(3(1 + 2z) + z(1 + 2z)) = 0
((1 * 3 + 2z * 3) + z(1 + 2z)) = 0
((3 + 6z) + z(1 + 2z)) = 0
(3 + 6z + (1 * z + 2z * z)) = 0
(3 + 6z + (1z + 2z2)) = 0

Combine like terms: 6z + 1z = 7z
(3 + 7z + 2z2) = 0

Solving
3 + 7z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(1 + 2z) = 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 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 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 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-3, -0.5}