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

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

Simplifying
(2n + 1)(n + -1) = 5

Reorder the terms:
(1 + 2n)(n + -1) = 5

Reorder the terms:
(1 + 2n)(-1 + n) = 5

Multiply (1 + 2n) * (-1 + n)
(1(-1 + n) + 2n * (-1 + n)) = 5
((-1 * 1 + n * 1) + 2n * (-1 + n)) = 5
((-1 + 1n) + 2n * (-1 + n)) = 5
(-1 + 1n + (-1 * 2n + n * 2n)) = 5
(-1 + 1n + (-2n + 2n2)) = 5

Combine like terms: 1n + -2n = -1n
(-1 + -1n + 2n2) = 5

Solving
-1 + -1n + 2n2 = 5

Solving for variable 'n'.

Reorder the terms:
-1 + -5 + -1n + 2n2 = 5 + -5

Combine like terms: -1 + -5 = -6
-6 + -1n + 2n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-6 + -1n + 2n2 = 0

Factor a trinomial.
(-3 + -2n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-1.5, 2}