(3z+2)(4+z)=0

Solution for (3z+2)(4+z)=0 equation:

Simplifying
(3z + 2)(4 + z) = 0

Reorder the terms:
(2 + 3z)(4 + z) = 0

Multiply (2 + 3z) * (4 + z)
(2(4 + z) + 3z * (4 + z)) = 0
((4 * 2 + z * 2) + 3z * (4 + z)) = 0
((8 + 2z) + 3z * (4 + z)) = 0
(8 + 2z + (4 * 3z + z * 3z)) = 0
(8 + 2z + (12z + 3z2)) = 0

Combine like terms: 2z + 12z = 14z
(8 + 14z + 3z2) = 0

Solving
8 + 14z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(2 + 3z) = 0

Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(2 + 3z)' equal to zero and attempt to solve:

Simplifying
2 + 3z = 0

Solving
2 + 3z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3z = 0 + -2
3z = 0 + -2

Combine like terms: 0 + -2 = -2
3z = -2

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Solution
z = {-4, -0.6666666667}