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

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

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

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

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