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

Solution for (5-z)(4z+1)=0 equation:

Simplifying
(5 + -1z)(4z + 1) = 0

Reorder the terms:
(5 + -1z)(1 + 4z) = 0

Multiply (5 + -1z) * (1 + 4z)
(5(1 + 4z) + -1z * (1 + 4z)) = 0
((1 * 5 + 4z * 5) + -1z * (1 + 4z)) = 0
((5 + 20z) + -1z * (1 + 4z)) = 0
(5 + 20z + (1 * -1z + 4z * -1z)) = 0
(5 + 20z + (-1z + -4z2)) = 0

Combine like terms: 20z + -1z = 19z
(5 + 19z + -4z2) = 0

Solving
5 + 19z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + -1z)(1 + 4z) = 0

Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
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 = {5, -0.25}