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

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

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

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

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

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

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

Solving
-1 + 4n + 5n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve:

Simplifying
1 + -5n = 0

Solving
1 + -5n = 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 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-1, 0.2}