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

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

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

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

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

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