SOLUTION: {{{n^3 -3n^2 + 2n = 210}}}

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Question 23624: n%5E3+-3n%5E2+%2B+2n+=+210
Found 2 solutions by kviji_85, Earlsdon:
Answer by kviji_85(2) About Me  (Show Source):
You can put this solution on YOUR website!
{n^3 -3n^2 + 2n = 210}
n(n^2-3n+2)=210
n(n^2-2n-n+2)=210
n(n(n-2) - (n-2)) = 210
n(n-1)(n-2)=10

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for n:
n%5E3-3n%5E2%2B2n+=+210 Subtract 210 from both sides of the equation.
n%5E3-3n%5E2%2B2n-210+=+0 Factor.
%28n-7%29%28n%5E2%2B4n%2B30%29+=+0 Apply the zero product principle.
n-7+=+0 and/or n%5E2%2B4n%2B30+=+0
If n-7+=+0 then n = 7 This is one of the three roots.
If n%5E2%2B4n%2B30+=+0 Use the quadratic formula to solve: n+=+%28-b%2B-sqrt%28b%5E2-4ac%29%2F2a%29
n+=+%28-4%2B-sqrt%284%5E2-4%281%29%2830%29%29%29%2F2%281%29
n+=+%28-4%2B-sqrt%2816-120%29%29%2F2
n+=+%28-4%2B-sqrt%28-104%29%29%2F2
n+=+%28-4%2B-sqrt%28-4%2A26%29%29%2F2
n+=+%28-4%2F2%29%2B%282sqrt%28-26%29%29%2F2 or n+=+%28-4%2F2%29-%282sqrt%28-26%29%29%2F2
n+=+-2%2Bsqrt%2826%29i or n+=+-2-sqrt%2826%29i
The three roots are:
n+=+7
n+=+-2%2Bsqrt%2826%29i
n+=+-2-sqrt%2826%29i
Here's the graph of the equation:
graph%28300%2C200%2C-10%2C10%2C-250%2C5%2Cx%5E3-3x%5E2%2B2x-210%29)