(5+n)(3+n)=63

Solution for (5+n)(3+n)=63 equation:

Simplifying
(5 + n)(3 + n) = 63

Multiply (5 + n) * (3 + n)
(5(3 + n) + n(3 + n)) = 63
((3 * 5 + n * 5) + n(3 + n)) = 63
((15 + 5n) + n(3 + n)) = 63
(15 + 5n + (3 * n + n * n)) = 63
(15 + 5n + (3n + n2)) = 63

Combine like terms: 5n + 3n = 8n
(15 + 8n + n2) = 63

Solving
15 + 8n + n2 = 63

Solving for variable 'n'.

Reorder the terms:
15 + -63 + 8n + n2 = 63 + -63

Combine like terms: 15 + -63 = -48
-48 + 8n + n2 = 63 + -63

Combine like terms: 63 + -63 = 0
-48 + 8n + n2 = 0

Factor a trinomial.
(-12 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1n = 0 + 12
-1n = 0 + 12

Combine like terms: 0 + 12 = 12
-1n = 12

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-12, 4}