5(2+n) = 3(n+6)

In order to to solve the equation and to find the value of
n for the identity to be tru, we'll follow the steps:

-
First, we'll remove the brackets, both sides:

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

10 + 5n = 3n + 18

-
Now, we'll isolate the terms that contain "n", to the left side. For this reason, we'll
subtract 3n both sides:

10 + 5n - 3n = 3n - 3n +
18

We'll reduce like terms and we'll
get:

10 + 2n = 0 + 18

 - Now,
we'll subtract 10 both sides:

10 + 2n - 10 = 18 -
10

We'll reduce like terms and we'll
get:

2n = 8

We'll divide by 2,
both sides:

n =
8/2

n =
4

So, the solution of the
given equation is n = 4.

- To verify the
equation, we'll input the value 4 in the given
expression:

5(2+4) =
3(4+6)

We'll calculate the sum in each pair of
brackets:

5 * 6 = 3 * 10

30 =
30

The identity is verified for n = 4, so the
solution n = 4 is valid.