(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 = 19z
(-4 + 19z + 5z2) = 0

Solving
-4 + 19z + 5z2 = 0

Solving for variable 'z'.

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