What is the answer to (n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18 ?

The answer to (n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18 is n=16

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(n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18

(n + 2) (n + 4) - (n + 1) (n + 5) + n^{2} + 3 n = (n + 1)^{2} + 18

n = 16

Solution steps

(n + 2) (n + 4) - (n + 1) (n + 5) + n^{2} + 3 n = (n + 1)^{2} + 18

Expand

(n + 2) (n + 4) - (n + 1) (n + 5) + n^{2} + 3 n : n^{2} + 3 n + 3

Expand

(n + 1)^{2} + 18 : n^{2} + 2 n + 19

n^{2} + 3 n + 3 = n^{2} + 2 n + 19

Move

3

to the right side

n^{2} + 3 n = n^{2} + 2 n + 16

Subtract

n^{2} + 2 n

from both sides

n^{2} + 3 n - (n^{2} + 2 n) = n^{2} + 2 n + 16 - (n^{2} + 2 n)

Simplify

n = 16

\frac{4}{3} x - 2 = \frac{2 x + 3}{3} - 1

4 x + 34 = 8 - 9 x

2.8 t - 7.6 = 0

7 q + 5 = 68

5 x - 1 = 4

What is the answer to (n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18 ?
The answer to (n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18 is n=16
Solve for n: (n+2)(n+4)-(n+1)(n+5)+n^2+3n=(n+1)^2+18
The solution is n=16