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

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

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

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

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

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

Solving
4 + 1z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -1z)(4 + 5z) = 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 '(4 + 5z)' equal to zero and attempt to solve:

Simplifying
4 + 5z = 0

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

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

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

Divide each side by '5'.
z = -0.8

Simplifying
z = -0.8
Solution
z = {1, -0.8}