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

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

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

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

Multiply (1 + 4z) * (4 + -1z)
(1(4 + -1z) + 4z * (4 + -1z)) = 0
((4 * 1 + -1z * 1) + 4z * (4 + -1z)) = 0
((4 + -1z) + 4z * (4 + -1z)) = 0
(4 + -1z + (4 * 4z + -1z * 4z)) = 0
(4 + -1z + (16z + -4z2)) = 0

Combine like terms: -1z + 16z = 15z
(4 + 15z + -4z2) = 0

Solving
4 + 15z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + -1z)(1 + 4z) = 0

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

Simplifying
4 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 4

Simplifying
z = 4
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 = {4, -0.25}