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

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

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

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

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

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

Solving
5 + -1z + -4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {1, -1.25}