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

Solution for (n+1)(6n+5)= equation:

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

Reorder the terms:
(1 + n)(6n + 5) = 0

Reorder the terms:
(1 + n)(5 + 6n) = 0

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

Combine like terms: 6n + 5n = 11n
(5 + 11n + 6n2) = 0

Solving
5 + 11n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + n)(5 + 6n) = 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 '(5 + 6n)' equal to zero and attempt to solve:

Simplifying
5 + 6n = 0

Solving
5 + 6n = 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 + 6n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6n = 0 + -5
6n = 0 + -5

Combine like terms: 0 + -5 = -5
6n = -5

Divide each side by '6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Solution
n = {-1, -0.8333333333}