(4z+1)(3+z)=0

Solution for (4z+1)(3+z)=0 equation:

Simplifying
(4z + 1)(3 + z) = 0

Reorder the terms:
(1 + 4z)(3 + z) = 0

Multiply (1 + 4z) * (3 + z)
(1(3 + z) + 4z * (3 + z)) = 0
((3 * 1 + z * 1) + 4z * (3 + z)) = 0
((3 + 1z) + 4z * (3 + z)) = 0
(3 + 1z + (3 * 4z + z * 4z)) = 0
(3 + 1z + (12z + 4z2)) = 0

Combine like terms: 1z + 12z = 13z
(3 + 13z + 4z2) = 0

Solving
3 + 13z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(1 + 4z) = 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 + 4z)' equal to zero and attempt to solve:

Simplifying
1 + 4z = 0

Solving
1 + 4z = 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 + 4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z = 0 + -1
4z = 0 + -1

Combine like terms: 0 + -1 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25
Solution
z = {-3, -0.25}