(n-2)(n-3)(n-4)(n-5)=360

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Solution for (n-2)(n-3)(n-4)(n-5)=360 equation: 


Simplifying
(n + -2)(n + -3)(n + -4)(n + -5) = 360

Reorder the terms:
(-2 + n)(n + -3)(n + -4)(n + -5) = 360

Reorder the terms:
(-2 + n)(-3 + n)(n + -4)(n + -5) = 360

Reorder the terms:
(-2 + n)(-3 + n)(-4 + n)(n + -5) = 360

Reorder the terms:
(-2 + n)(-3 + n)(-4 + n)(-5 + n) = 360

Multiply (-2 + n) * (-3 + n)
(-2(-3 + n) + n(-3 + n))(-4 + n)(-5 + n) = 360
((-3 * -2 + n * -2) + n(-3 + n))(-4 + n)(-5 + n) = 360
((6 + -2n) + n(-3 + n))(-4 + n)(-5 + n) = 360
(6 + -2n + (-3 * n + n * n))(-4 + n)(-5 + n) = 360
(6 + -2n + (-3n + n2))(-4 + n)(-5 + n) = 360

Combine like terms: -2n + -3n = -5n
(6 + -5n + n2)(-4 + n)(-5 + n) = 360

Multiply (6 + -5n + n2) * (-4 + n)
(6(-4 + n) + -5n * (-4 + n) + n2(-4 + n))(-5 + n) = 360
((-4 * 6 + n * 6) + -5n * (-4 + n) + n2(-4 + n))(-5 + n) = 360
((-24 + 6n) + -5n * (-4 + n) + n2(-4 + n))(-5 + n) = 360
(-24 + 6n + (-4 * -5n + n * -5n) + n2(-4 + n))(-5 + n) = 360
(-24 + 6n + (20n + -5n2) + n2(-4 + n))(-5 + n) = 360
(-24 + 6n + 20n + -5n2 + (-4 * n2 + n * n2))(-5 + n) = 360
(-24 + 6n + 20n + -5n2 + (-4n2 + n3))(-5 + n) = 360

Combine like terms: 6n + 20n = 26n
(-24 + 26n + -5n2 + -4n2 + n3)(-5 + n) = 360

Combine like terms: -5n2 + -4n2 = -9n2
(-24 + 26n + -9n2 + n3)(-5 + n) = 360

Multiply (-24 + 26n + -9n2 + n3) * (-5 + n)
(-24(-5 + n) + 26n * (-5 + n) + -9n2 * (-5 + n) + n3(-5 + n)) = 360
((-5 * -24 + n * -24) + 26n * (-5 + n) + -9n2 * (-5 + n) + n3(-5 + n)) = 360
((120 + -24n) + 26n * (-5 + n) + -9n2 * (-5 + n) + n3(-5 + n)) = 360
(120 + -24n + (-5 * 26n + n * 26n) + -9n2 * (-5 + n) + n3(-5 + n)) = 360
(120 + -24n + (-130n + 26n2) + -9n2 * (-5 + n) + n3(-5 + n)) = 360
(120 + -24n + -130n + 26n2 + (-5 * -9n2 + n * -9n2) + n3(-5 + n)) = 360
(120 + -24n + -130n + 26n2 + (45n2 + -9n3) + n3(-5 + n)) = 360
(120 + -24n + -130n + 26n2 + 45n2 + -9n3 + (-5 * n3 + n * n3)) = 360
(120 + -24n + -130n + 26n2 + 45n2 + -9n3 + (-5n3 + n4)) = 360

Combine like terms: -24n + -130n = -154n
(120 + -154n + 26n2 + 45n2 + -9n3 + -5n3 + n4) = 360

Combine like terms: 26n2 + 45n2 = 71n2
(120 + -154n + 71n2 + -9n3 + -5n3 + n4) = 360

Combine like terms: -9n3 + -5n3 = -14n3
(120 + -154n + 71n2 + -14n3 + n4) = 360

Solving
120 + -154n + 71n2 + -14n3 + n4 = 360

Solving for variable 'n'.

Reorder the terms:
120 + -360 + -154n + 71n2 + -14n3 + n4 = 360 + -360

Combine like terms: 120 + -360 = -240
-240 + -154n + 71n2 + -14n3 + n4 = 360 + -360

Combine like terms: 360 + -360 = 0
-240 + -154n + 71n2 + -14n3 + n4 = 0

The solution to this equation could not be determined.

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