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

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

Simplifying
2n(n + 1) + -5(n + 1) = 0

Reorder the terms:
2n(1 + n) + -5(n + 1) = 0
(1 * 2n + n * 2n) + -5(n + 1) = 0
(2n + 2n2) + -5(n + 1) = 0

Reorder the terms:
2n + 2n2 + -5(1 + n) = 0
2n + 2n2 + (1 * -5 + n * -5) = 0
2n + 2n2 + (-5 + -5n) = 0

Reorder the terms:
-5 + 2n + -5n + 2n2 = 0

Combine like terms: 2n + -5n = -3n
-5 + -3n + 2n2 = 0

Solving
-5 + -3n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(5 + -2n) = 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 '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 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 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {-1, 2.5}