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

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

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

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

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

Combine like terms: 4z + 5z = 9z
(-5 + 9z + -4z2) = 0

Solving
-5 + 9z + -4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(-5 + 4z)' equal to zero and attempt to solve:

Simplifying
-5 + 4z = 0

Solving
-5 + 4z = 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 + 4z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4z = 0 + 5
4z = 0 + 5

Combine like terms: 0 + 5 = 5
4z = 5

Divide each side by '4'.
z = 1.25

Simplifying
z = 1.25
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {1.25, 1}