(n+5)(n+2)4=280

Solution for (n+5)(n+2)4=280 equation:

Simplifying
(n + 5)(n + 2) * 4 = 280

Reorder the terms:
(5 + n)(n + 2) * 4 = 280

Reorder the terms:
(5 + n)(2 + n) * 4 = 280

Reorder the terms for easier multiplication:
4(5 + n)(2 + n) = 280

Multiply (5 + n) * (2 + n)
4(5(2 + n) + n(2 + n)) = 280
4((2 * 5 + n * 5) + n(2 + n)) = 280
4((10 + 5n) + n(2 + n)) = 280
4(10 + 5n + (2 * n + n * n)) = 280
4(10 + 5n + (2n + n2)) = 280

Combine like terms: 5n + 2n = 7n
4(10 + 7n + n2) = 280
(10 * 4 + 7n * 4 + n2 * 4) = 280
(40 + 28n + 4n2) = 280

Solving
40 + 28n + 4n2 = 280

Solving for variable 'n'.

Reorder the terms:
40 + -280 + 28n + 4n2 = 280 + -280

Combine like terms: 40 + -280 = -240
-240 + 28n + 4n2 = 280 + -280

Combine like terms: 280 + -280 = 0
-240 + 28n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 7n + n2) = 0

Factor a trinomial.
4((-12 + -1n)(5 + -1n)) = 0

Ignore the factor 4.
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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-12, 5}