document.write( "Question 23624: $\"n%5E3+-3n%5E2+%2B+2n+=+210\"$ \n" ); document.write( "

Algebra.Com's Answer #12413 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for n:\r
\n" ); document.write( "\n" ); document.write( " $\"n%5E3-3n%5E2%2B2n+=+210\"$ Subtract 210 from both sides of the equation.
\n" ); document.write( " $\"n%5E3-3n%5E2%2B2n-210+=+0\"$ Factor.
\n" ); document.write( " $\"%28n-7%29%28n%5E2%2B4n%2B30%29+=+0\"$ Apply the zero product principle.
\n" ); document.write( " $\"n-7+=+0\"$ and/or $\"n%5E2%2B4n%2B30+=+0\"$
\n" ); document.write( "If $\"n-7+=+0\"$ then n = 7 This is one of the three roots.
\n" ); document.write( "If $\"n%5E2%2B4n%2B30+=+0\"$ Use the quadratic formula to solve: $\"n+=+%28-b%2B-sqrt%28b%5E2-4ac%29%2F2a%29\"$
\n" ); document.write( " $\"n+=+%28-4%2B-sqrt%284%5E2-4%281%29%2830%29%29%29%2F2%281%29\"$
\n" ); document.write( " $\"n+=+%28-4%2B-sqrt%2816-120%29%29%2F2\"$
\n" ); document.write( " $\"n+=+%28-4%2B-sqrt%28-104%29%29%2F2\"$
\n" ); document.write( " $\"n+=+%28-4%2B-sqrt%28-4%2A26%29%29%2F2\"$
\n" ); document.write( " $\"n+=+%28-4%2F2%29%2B%282sqrt%28-26%29%29%2F2\"$ or $\"n+=+%28-4%2F2%29-%282sqrt%28-26%29%29%2F2\"$
\n" ); document.write( " $\"n+=+-2%2Bsqrt%2826%29i\"$ or $\"n+=+-2-sqrt%2826%29i\"$ \r
\n" ); document.write( "\n" ); document.write( "The three roots are:
\n" ); document.write( " $\"n+=+7\"$
\n" ); document.write( " $\"n+=+-2%2Bsqrt%2826%29i\"$
\n" ); document.write( " $\"n+=+-2-sqrt%2826%29i\"$ \r
\n" ); document.write( "\n" ); document.write( "Here's the graph of the equation:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-250%2C5%2Cx%5E3-3x%5E2%2B2x-210%29\"$ ) \n" ); document.write( "

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