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

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

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

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

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

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

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

Solving
5 + -21z + 4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {0.25, 5}