(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 = 6n
(1 + 6n + 5n2) = 0

Solving
1 + 6n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
1 + n = 0

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

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

Combine like terms: 0 + -1 = -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}