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

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

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

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

Multiply (3 + 4z) * (2 + z)
(3(2 + z) + 4z * (2 + z)) = 0
((2 * 3 + z * 3) + 4z * (2 + z)) = 0
((6 + 3z) + 4z * (2 + z)) = 0
(6 + 3z + (2 * 4z + z * 4z)) = 0
(6 + 3z + (8z + 4z2)) = 0

Combine like terms: 3z + 8z = 11z
(6 + 11z + 4z2) = 0

Solving
6 + 11z + 4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

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

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

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

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

Simplifying
3 + 4z = 0

Solving
3 + 4z = 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 + 4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4z = 0 + -3
4z = 0 + -3

Combine like terms: 0 + -3 = -3
4z = -3

Divide each side by '4'.
z = -0.75

Simplifying
z = -0.75
Solution
z = {-2, -0.75}