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

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

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

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

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

Multiply (5 + 4n) * (-1 + n)
(5(-1 + n) + 4n * (-1 + n)) = 0
((-1 * 5 + n * 5) + 4n * (-1 + n)) = 0
((-5 + 5n) + 4n * (-1 + n)) = 0
(-5 + 5n + (-1 * 4n + n * 4n)) = 0
(-5 + 5n + (-4n + 4n2)) = 0

Combine like terms: 5n + -4n = 1n
(-5 + 1n + 4n2) = 0

Solving
-5 + 1n + 4n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -4n = 0

Solving
-5 + -4n = 0

Move all terms containing n to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -4n = 0 + 5

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

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

Divide each side by '-4'.
n = -1.25

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-1.25, 1}