5n(2+n)=6n+1

Solution for 5n(2+n)=6n+1 equation:

Simplifying
5n(2 + n) = 6n + 1
(2 * 5n + n * 5n) = 6n + 1
(10n + 5n2) = 6n + 1

Reorder the terms:
10n + 5n2 = 1 + 6n

Solving
10n + 5n2 = 1 + 6n

Solving for variable 'n'.

Reorder the terms:
-1 + 10n + -6n + 5n2 = 1 + 6n + -1 + -6n

Combine like terms: 10n + -6n = 4n
-1 + 4n + 5n2 = 1 + 6n + -1 + -6n

Reorder the terms:
-1 + 4n + 5n2 = 1 + -1 + 6n + -6n

Combine like terms: 1 + -1 = 0
-1 + 4n + 5n2 = 0 + 6n + -6n
-1 + 4n + 5n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-1 + 4n + 5n2 = 0

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}