(n-5)(n+3)=48

Solution for (n-5)(n+3)=48 equation:

Simplifying
(n + -5)(n + 3) = 48

Reorder the terms:
(-5 + n)(n + 3) = 48

Reorder the terms:
(-5 + n)(3 + n) = 48

Multiply (-5 + n) * (3 + n)
(-5(3 + n) + n(3 + n)) = 48
((3 * -5 + n * -5) + n(3 + n)) = 48
((-15 + -5n) + n(3 + n)) = 48
(-15 + -5n + (3 * n + n * n)) = 48
(-15 + -5n + (3n + n2)) = 48

Combine like terms: -5n + 3n = -2n
(-15 + -2n + n2) = 48

Solving
-15 + -2n + n2 = 48

Solving for variable 'n'.

Reorder the terms:
-15 + -48 + -2n + n2 = 48 + -48

Combine like terms: -15 + -48 = -63
-63 + -2n + n2 = 48 + -48

Combine like terms: 48 + -48 = 0
-63 + -2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

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

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

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-7, 9}