12=(n-1)(n-2)(n-3)(n-4)(n-5)-3n^2

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Solution for 12=(n-1)(n-2)(n-3)(n-4)(n-5)-3n^2 equation:


Simplifying
12 = (n + -1)(n + -2)(n + -3)(n + -4)(n + -5) + -3n2

Reorder the terms:
12 = (-1 + n)(n + -2)(n + -3)(n + -4)(n + -5) + -3n2

Reorder the terms:
12 = (-1 + n)(-2 + n)(n + -3)(n + -4)(n + -5) + -3n2

Reorder the terms:
12 = (-1 + n)(-2 + n)(-3 + n)(n + -4)(n + -5) + -3n2

Reorder the terms:
12 = (-1 + n)(-2 + n)(-3 + n)(-4 + n)(n + -5) + -3n2

Reorder the terms:
12 = (-1 + n)(-2 + n)(-3 + n)(-4 + n)(-5 + n) + -3n2

Multiply (-1 + n) * (-2 + n)
12 = (-1(-2 + n) + n(-2 + n))(-3 + n)(-4 + n)(-5 + n) + -3n2
12 = ((-2 * -1 + n * -1) + n(-2 + n))(-3 + n)(-4 + n)(-5 + n) + -3n2
12 = ((2 + -1n) + n(-2 + n))(-3 + n)(-4 + n)(-5 + n) + -3n2
12 = (2 + -1n + (-2 * n + n * n))(-3 + n)(-4 + n)(-5 + n) + -3n2
12 = (2 + -1n + (-2n + n2))(-3 + n)(-4 + n)(-5 + n) + -3n2

Combine like terms: -1n + -2n = -3n
12 = (2 + -3n + n2)(-3 + n)(-4 + n)(-5 + n) + -3n2

Multiply (2 + -3n + n2) * (-3 + n)
12 = (2(-3 + n) + -3n * (-3 + n) + n2(-3 + n))(-4 + n)(-5 + n) + -3n2
12 = ((-3 * 2 + n * 2) + -3n * (-3 + n) + n2(-3 + n))(-4 + n)(-5 + n) + -3n2
12 = ((-6 + 2n) + -3n * (-3 + n) + n2(-3 + n))(-4 + n)(-5 + n) + -3n2
12 = (-6 + 2n + (-3 * -3n + n * -3n) + n2(-3 + n))(-4 + n)(-5 + n) + -3n2
12 = (-6 + 2n + (9n + -3n2) + n2(-3 + n))(-4 + n)(-5 + n) + -3n2
12 = (-6 + 2n + 9n + -3n2 + (-3 * n2 + n * n2))(-4 + n)(-5 + n) + -3n2
12 = (-6 + 2n + 9n + -3n2 + (-3n2 + n3))(-4 + n)(-5 + n) + -3n2

Combine like terms: 2n + 9n = 11n
12 = (-6 + 11n + -3n2 + -3n2 + n3)(-4 + n)(-5 + n) + -3n2

Combine like terms: -3n2 + -3n2 = -6n2
12 = (-6 + 11n + -6n2 + n3)(-4 + n)(-5 + n) + -3n2

Multiply (-6 + 11n + -6n2 + n3) * (-4 + n)
12 = (-6(-4 + n) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n))(-5 + n) + -3n2
12 = ((-4 * -6 + n * -6) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n))(-5 + n) + -3n2
12 = ((24 + -6n) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n))(-5 + n) + -3n2
12 = (24 + -6n + (-4 * 11n + n * 11n) + -6n2 * (-4 + n) + n3(-4 + n))(-5 + n) + -3n2
12 = (24 + -6n + (-44n + 11n2) + -6n2 * (-4 + n) + n3(-4 + n))(-5 + n) + -3n2
12 = (24 + -6n + -44n + 11n2 + (-4 * -6n2 + n * -6n2) + n3(-4 + n))(-5 + n) + -3n2
12 = (24 + -6n + -44n + 11n2 + (24n2 + -6n3) + n3(-4 + n))(-5 + n) + -3n2
12 = (24 + -6n + -44n + 11n2 + 24n2 + -6n3 + (-4 * n3 + n * n3))(-5 + n) + -3n2
12 = (24 + -6n + -44n + 11n2 + 24n2 + -6n3 + (-4n3 + n4))(-5 + n) + -3n2

Combine like terms: -6n + -44n = -50n
12 = (24 + -50n + 11n2 + 24n2 + -6n3 + -4n3 + n4)(-5 + n) + -3n2

Combine like terms: 11n2 + 24n2 = 35n2
12 = (24 + -50n + 35n2 + -6n3 + -4n3 + n4)(-5 + n) + -3n2

Combine like terms: -6n3 + -4n3 = -10n3
12 = (24 + -50n + 35n2 + -10n3 + n4)(-5 + n) + -3n2

Multiply (24 + -50n + 35n2 + -10n3 + n4) * (-5 + n)
12 = (24(-5 + n) + -50n * (-5 + n) + 35n2 * (-5 + n) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = ((-5 * 24 + n * 24) + -50n * (-5 + n) + 35n2 * (-5 + n) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = ((-120 + 24n) + -50n * (-5 + n) + 35n2 * (-5 + n) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + (-5 * -50n + n * -50n) + 35n2 * (-5 + n) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + (250n + -50n2) + 35n2 * (-5 + n) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + (-5 * 35n2 + n * 35n2) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + (-175n2 + 35n3) + -10n3 * (-5 + n) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + -175n2 + 35n3 + (-5 * -10n3 + n * -10n3) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + -175n2 + 35n3 + (50n3 + -10n4) + n4(-5 + n)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + -175n2 + 35n3 + 50n3 + -10n4 + (-5 * n4 + n * n4)) + -3n2
12 = (-120 + 24n + 250n + -50n2 + -175n2 + 35n3 + 50n3 + -10n4 + (-5n4 + n5)) + -3n2

Combine like terms: 24n + 250n = 274n
12 = (-120 + 274n + -50n2 + -175n2 + 35n3 + 50n3 + -10n4 + -5n4 + n5) + -3n2

Combine like terms: -50n2 + -175n2 = -225n2
12 = (-120 + 274n + -225n2 + 35n3 + 50n3 + -10n4 + -5n4 + n5) + -3n2

Combine like terms: 35n3 + 50n3 = 85n3
12 = (-120 + 274n + -225n2 + 85n3 + -10n4 + -5n4 + n5) + -3n2

Combine like terms: -10n4 + -5n4 = -15n4
12 = (-120 + 274n + -225n2 + 85n3 + -15n4 + n5) + -3n2

Reorder the terms:
12 = -120 + 274n + -225n2 + -3n2 + 85n3 + -15n4 + n5

Combine like terms: -225n2 + -3n2 = -228n2
12 = -120 + 274n + -228n2 + 85n3 + -15n4 + n5

Solving
12 = -120 + 274n + -228n2 + 85n3 + -15n4 + n5

Solving for variable 'n'.

Combine like terms: 12 + 120 = 132
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = -120 + 274n + -228n2 + 85n3 + -15n4 + n5 + 120 + -274n + 228n2 + -85n3 + 15n4 + -1n5

Reorder the terms:
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = -120 + 120 + 274n + -274n + -228n2 + 228n2 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5

Combine like terms: -120 + 120 = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0 + 274n + -274n + -228n2 + 228n2 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 274n + -274n + -228n2 + 228n2 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5

Combine like terms: 274n + -274n = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0 + -228n2 + 228n2 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = -228n2 + 228n2 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5

Combine like terms: -228n2 + 228n2 = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0 + 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 85n3 + -85n3 + -15n4 + 15n4 + n5 + -1n5

Combine like terms: 85n3 + -85n3 = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0 + -15n4 + 15n4 + n5 + -1n5
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = -15n4 + 15n4 + n5 + -1n5

Combine like terms: -15n4 + 15n4 = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0 + n5 + -1n5
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = n5 + -1n5

Combine like terms: n5 + -1n5 = 0
132 + -274n + 228n2 + -85n3 + 15n4 + -1n5 = 0

The solution to this equation could not be determined.

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