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

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

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

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

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

Combine like terms: 20z + 1z = 21z
(4 + 21z + 5z2) = 0

Solving
4 + 21z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(1 + 5z) = 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 '(1 + 5z)' equal to zero and attempt to solve:

Simplifying
1 + 5z = 0

Solving
1 + 5z = 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 + 5z = 0 + -1

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

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

Divide each side by '5'.
z = -0.2

Simplifying
z = -0.2
Solution
z = {-4, -0.2}