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

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

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

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

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

Combine like terms: 3z + 8z = 11z
(12 + 11z + 2z2) = 0

Solving
12 + 11z + 2z2 = 0

Solving for variable 'z'.

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

Simplifying
3 + 2z = 0

Solving
3 + 2z = 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 + 2z = 0 + -3

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

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

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {-4, -1.5}