2n(n+3)-5(n+3)=

Solution for 2n(n+3)-5(n+3)= equation:

Simplifying
2n(n + 3) + -5(n + 3) = 0

Reorder the terms:
2n(3 + n) + -5(n + 3) = 0
(3 * 2n + n * 2n) + -5(n + 3) = 0
(6n + 2n2) + -5(n + 3) = 0

Reorder the terms:
6n + 2n2 + -5(3 + n) = 0
6n + 2n2 + (3 * -5 + n * -5) = 0
6n + 2n2 + (-15 + -5n) = 0

Reorder the terms:
-15 + 6n + -5n + 2n2 = 0

Combine like terms: 6n + -5n = 1n
-15 + 1n + 2n2 = 0

Solving
-15 + 1n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(5 + -2n) = 0

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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 = {-3, 2.5}