(n+4)(n+2)=(n+1)(n+6)

Solution for (n+4)(n+2)=(n+1)(n+6) equation:

Simplifying
(n + 4)(n + 2) = (n + 1)(n + 6)

Reorder the terms:
(4 + n)(n + 2) = (n + 1)(n + 6)

Reorder the terms:
(4 + n)(2 + n) = (n + 1)(n + 6)

Multiply (4 + n) * (2 + n)
(4(2 + n) + n(2 + n)) = (n + 1)(n + 6)
((2 * 4 + n * 4) + n(2 + n)) = (n + 1)(n + 6)
((8 + 4n) + n(2 + n)) = (n + 1)(n + 6)
(8 + 4n + (2 * n + n * n)) = (n + 1)(n + 6)
(8 + 4n + (2n + n2)) = (n + 1)(n + 6)

Combine like terms: 4n + 2n = 6n
(8 + 6n + n2) = (n + 1)(n + 6)

Reorder the terms:
8 + 6n + n2 = (1 + n)(n + 6)

Reorder the terms:
8 + 6n + n2 = (1 + n)(6 + n)

Multiply (1 + n) * (6 + n)
8 + 6n + n2 = (1(6 + n) + n(6 + n))
8 + 6n + n2 = ((6 * 1 + n * 1) + n(6 + n))
8 + 6n + n2 = ((6 + 1n) + n(6 + n))
8 + 6n + n2 = (6 + 1n + (6 * n + n * n))
8 + 6n + n2 = (6 + 1n + (6n + n2))

Combine like terms: 1n + 6n = 7n
8 + 6n + n2 = (6 + 7n + n2)

Add '-1n2' to each side of the equation.
8 + 6n + n2 + -1n2 = 6 + 7n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
8 + 6n + 0 = 6 + 7n + n2 + -1n2
8 + 6n = 6 + 7n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
8 + 6n = 6 + 7n + 0
8 + 6n = 6 + 7n

Solving
8 + 6n = 6 + 7n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-7n' to each side of the equation.
8 + 6n + -7n = 6 + 7n + -7n

Combine like terms: 6n + -7n = -1n
8 + -1n = 6 + 7n + -7n

Combine like terms: 7n + -7n = 0
8 + -1n = 6 + 0
8 + -1n = 6

Add '-8' to each side of the equation.
8 + -8 + -1n = 6 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 6 + -8
-1n = 6 + -8

Combine like terms: 6 + -8 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2