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

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


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

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

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

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

Multiply x * x
280 = 4x2(2 + n)(5 + n)

Multiply (2 + n) * (5 + n)
280 = 4x2(2(5 + n) + n(5 + n))
280 = 4x2((5 * 2 + n * 2) + n(5 + n))
280 = 4x2((10 + 2n) + n(5 + n))
280 = 4x2(10 + 2n + (5 * n + n * n))
280 = 4x2(10 + 2n + (5n + n2))

Combine like terms: 2n + 5n = 7n
280 = 4x2(10 + 7n + n2)
280 = (10 * 4x2 + 7n * 4x2 + n2 * 4x2)

Reorder the terms:
280 = (28nx2 + 4n2x2 + 40x2)
280 = (28nx2 + 4n2x2 + 40x2)

Solving
280 = 28nx2 + 4n2x2 + 40x2

Solving for variable 'n'.

Reorder the terms:
280 + -28nx2 + -4n2x2 + -40x2 = 28nx2 + -28nx2 + 4n2x2 + -4n2x2 + 40x2 + -40x2

Combine like terms: 28nx2 + -28nx2 = 0
280 + -28nx2 + -4n2x2 + -40x2 = 0 + 4n2x2 + -4n2x2 + 40x2 + -40x2
280 + -28nx2 + -4n2x2 + -40x2 = 4n2x2 + -4n2x2 + 40x2 + -40x2

Combine like terms: 4n2x2 + -4n2x2 = 0
280 + -28nx2 + -4n2x2 + -40x2 = 0 + 40x2 + -40x2
280 + -28nx2 + -4n2x2 + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
280 + -28nx2 + -4n2x2 + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(70 + -7nx2 + -1n2x2 + -10x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(70 + -7nx2 + -1n2x2 + -10x2)' equal to zero and attempt to solve:

Simplifying
70 + -7nx2 + -1n2x2 + -10x2 = 0

Solving
70 + -7nx2 + -1n2x2 + -10x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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