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

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


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

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

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

Multiply (2 + n) * (5 + n)
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)) = -280

Combine like terms: 2n + 5n = 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 = 320
320 + 28n + 4n2 = -280 + 280

Combine like terms: -280 + 280 = 0
320 + 28n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(80 + 7n + n2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(80 + 7n + n2)' equal to zero and attempt to solve: Simplifying 80 + 7n + n2 = 0 Solving 80 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 7n + -80 + n2 = 0 + -80 Reorder the terms: 80 + -80 + 7n + n2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 7n + n2 = 0 + -80 7n + n2 = 0 + -80 Combine like terms: 0 + -80 = -80 7n + n2 = -80 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = -80 + 12.25 Reorder the terms: 12.25 + 7n + n2 = -80 + 12.25 Combine like terms: -80 + 12.25 = -67.75 12.25 + 7n + n2 = -67.75 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = -67.75 Can't calculate square root of the right side. 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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