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

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

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

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

Multiply (4 + z) * (3 + 4z)
(4(3 + 4z) + z(3 + 4z)) = 0
((3 * 4 + 4z * 4) + z(3 + 4z)) = 0
((12 + 16z) + z(3 + 4z)) = 0
(12 + 16z + (3 * z + 4z * z)) = 0
(12 + 16z + (3z + 4z2)) = 0

Combine like terms: 16z + 3z = 19z
(12 + 19z + 4z2) = 0

Solving
12 + 19z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(3 + 4z) = 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 + 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 = {-4, -0.75}