Solve for the variable
1 + 3n + 7n = 7(n + 4) + 6(3n + 3)

1 + 3n + 7n = 7(n + 4) + 6(3n + 3)
1 + 3n + 7n = 7n + 28  + 18n + 18
10n + 1 = 25n +46
25n - 10n = 1 - 46
15n = -45
n = -45/15
n =-3

1 + 3n + 7n = 7(n+4) + 6(3n + 3)

In the first side of the equation: 1 + 3n + 7n
You can see that there's the addition of the same variable but with different coefficients. Their addition gives the same variable with the addition of the coefficients:
1 + 3n + 7n = 1 + (3+7)n = 1 + 10n

In the second side of the equation: 7(n+4) + 6(3n + 3)
Let's develop both parts of equation:
7(n+4) = 7n + 28
6(3n + 3) = 18n + 18
So 7(n+4) + 6(3n + 3) = 7n + 28 + 18n + 18
Same thing as the first side, you add the variables between each others and the numbers between each others:
7n + 18n + 28 + 18 = 25n + 46

So we can now retype the equation:
1 + 3n + 7n = 7(n+4) + 6(3n+3)
1 + 10n = 25n + 46
Now to solve for n, you need to have the variables on a side and the numbers on the other. So first subtract 25n from each side:
1 + 10n - 25n = 25n - 25n + 46
1 + 10n - 25n = 46
Then subtract 1 from each side:
1 + 10n - 25n -1 = 46 - 1
10n - 25n = 46 - 1
Now simple calculus:
- 15n = 45
Now divide each side by -15 to get the variable n alone on a side and its value on the other side:
(-15n)/-15 = 45/-15
n = -3

You can recheck your answer (very important):
1 + 3n + 7n = 1 + 3(-3) + 7(-3) = 1 - 9 - 21 = -29
7(n+4) + 6(3n + 3) = 7(-3+4) + 6(3*-3 + 3) = 7 + 6*-6 = 7 - 36 = -29
So 1 + 3n + 7n = 7(n+4)+6(3n+3) = -29
The answer has been approved.

Hope this Helps! :)