(n+4-7)*(n+4)=30

Solution for (n+4-7)*(n+4)=30 equation:

Simplifying
(n + 4 + -7)(n + 4) = 30

Reorder the terms:
(4 + -7 + n)(n + 4) = 30

Combine like terms: 4 + -7 = -3
(-3 + n)(n + 4) = 30

Reorder the terms:
(-3 + n)(4 + n) = 30

Multiply (-3 + n) * (4 + n)
(-3(4 + n) + n(4 + n)) = 30
((4 * -3 + n * -3) + n(4 + n)) = 30
((-12 + -3n) + n(4 + n)) = 30
(-12 + -3n + (4 * n + n * n)) = 30
(-12 + -3n + (4n + n2)) = 30

Combine like terms: -3n + 4n = 1n
(-12 + 1n + n2) = 30

Solving
-12 + 1n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-12 + -30 + 1n + n2 = 30 + -30

Combine like terms: -12 + -30 = -42
-42 + 1n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-42 + 1n + n2 = 0

Factor a trinomial.
(-7 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

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

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

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-7, 6}