(n+4)(n+4-7)=60

Solution for (n+4)(n+4-7)=60 equation:

Simplifying
(n + 4)(n + 4 + -7) = 60

Reorder the terms:
(4 + n)(n + 4 + -7) = 60

Reorder the terms:
(4 + n)(4 + -7 + n) = 60

Combine like terms: 4 + -7 = -3
(4 + n)(-3 + n) = 60

Multiply (4 + n) * (-3 + n)
(4(-3 + n) + n(-3 + n)) = 60
((-3 * 4 + n * 4) + n(-3 + n)) = 60
((-12 + 4n) + n(-3 + n)) = 60
(-12 + 4n + (-3 * n + n * n)) = 60
(-12 + 4n + (-3n + n2)) = 60

Combine like terms: 4n + -3n = 1n
(-12 + 1n + n2) = 60

Solving
-12 + 1n + n2 = 60

Solving for variable 'n'.

Reorder the terms:
-12 + -60 + 1n + n2 = 60 + -60

Combine like terms: -12 + -60 = -72
-72 + 1n + n2 = 60 + -60

Combine like terms: 60 + -60 = 0
-72 + 1n + n2 = 0

Factor a trinomial.
(-9 + -1n)(8 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

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

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

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-9, 8}