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

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


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

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

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

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

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

Solving
280 = 40 + 28n + 4n2

Solving for variable 'n'.

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

Reorder the terms:
240 + -28n + -4n2 = 40 + -40 + 28n + -28n + 4n2 + -4n2

Combine like terms: 40 + -40 = 0
240 + -28n + -4n2 = 0 + 28n + -28n + 4n2 + -4n2
240 + -28n + -4n2 = 28n + -28n + 4n2 + -4n2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(60 + -7n + -1n2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 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 + n = 0 + -12

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

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

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

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