2n(n-1)(n-2)=84n

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Solution for 2n(n-1)(n-2)=84n equation: 


Simplifying
2n(n + -1)(n + -2) = 84n

Reorder the terms:
2n(-1 + n)(n + -2) = 84n

Reorder the terms:
2n(-1 + n)(-2 + n) = 84n

Multiply (-1 + n) * (-2 + n)
2n(-1(-2 + n) + n(-2 + n)) = 84n
2n((-2 * -1 + n * -1) + n(-2 + n)) = 84n
2n((2 + -1n) + n(-2 + n)) = 84n
2n(2 + -1n + (-2 * n + n * n)) = 84n
2n(2 + -1n + (-2n + n2)) = 84n

Combine like terms: -1n + -2n = -3n
2n(2 + -3n + n2) = 84n
(2 * 2n + -3n * 2n + n2 * 2n) = 84n
(4n + -6n2 + 2n3) = 84n

Solving
4n + -6n2 + 2n3 = 84n

Solving for variable 'n'.

Reorder the terms:
4n + -84n + -6n2 + 2n3 = 84n + -84n

Combine like terms: 4n + -84n = -80n
-80n + -6n2 + 2n3 = 84n + -84n

Combine like terms: 84n + -84n = 0
-80n + -6n2 + 2n3 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-40 + -3n + n2) = 0

Factor a trinomial.
2n((-5 + -1n)(8 + -1n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
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 3
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {0, -5, 8}

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