document.write( "Question 306892: a rectangular box has volume 280^3in. its dimensions are 4in. x(n+2)in. x(n+5)in. find n. use the formula v=lwh \n" ); document.write( "

Algebra.Com's Answer #219563 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
4*(n+2)*(n+5)=280
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: n=5,n=-12.
Graphical form: Equation $\"4%2A%28n%2B2%29%2A%28n%2B5%29=280\"$ was fully solved.
Text form: 4*(n+2)*(n+5)=280 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+4%2A%28n%2B2%29%2A%28n%2B5%29=280+%29\"$
For tutors: simplify_cartoon( 4*(n+2)*(n+5)=280 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"4%2A%28n%2B2%29%2A%28n%2B5%29=highlight_red%28+280+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-280+%29\"$
It becomes $\"4%2A%28n%2B2%29%2A%28n%2B5%29-highlight_green%28+280+%29=0\"$ .
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Look at $\"highlight_red%28+4%2A%28n%2B2%29%2A%28n%2B5%29+%29-280=0\"$ .
Expanded term $\"4%2A%28n%2B5%29\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes

.
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Look at $\"4%2A%28n%2B5%29%2An%2Bhighlight_red%28+4+%29%2A%28n%2B5%29%2Ahighlight_red%28+2+%29-280=0\"$ .
Multiplied numerator integers
It becomes $\"4%2A%28n%2B5%29%2An%2Bhighlight_green%28+8+%29%2A%28n%2B5%29-280=0\"$ .
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Look at $\"highlight_red%28+4%2A%28n%2B5%29%2An+%29%2B8%2A%28n%2B5%29-280=0\"$ .
Expanded term $\"4%2An\"$ by using associative property on $\"%28n%2B5%29\"$
It becomes $\"highlight_green%28+4%2An%2An+%29%2Bhighlight_green%28+4%2An%2A5+%29%2B8%2A%28n%2B5%29-280=0\"$ .
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Look at $\"4%2An%2An%2Bhighlight_red%28+4+%29%2An%2Ahighlight_red%28+5+%29%2B8%2A%28n%2B5%29-280=0\"$ .
Multiplied numerator integers
It becomes $\"4%2An%2An%2Bhighlight_green%28+20+%29%2An%2B8%2A%28n%2B5%29-280=0\"$ .
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Look at $\"4%2Ahighlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2B20%2An%2B8%2A%28n%2B5%29-280=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+n+%29\"$ to $\"highlight_green%28+n%5E2+%29\"$
It becomes $\"4%2Ahighlight_green%28+n%5E2+%29%2B20%2An%2B8%2A%28n%2B5%29-280=0\"$ .
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Look at $\"4%2An%5E2%2B20%2An%2Bhighlight_red%28+8%2A%28n%2B5%29+%29-280=0\"$ .
Expanded term $\"8\"$ by using associative property on $\"%28n%2B5%29\"$
It becomes $\"4%2An%5E2%2B20%2An%2Bhighlight_green%28+8%2An+%29%2Bhighlight_green%28+8%2A5+%29-280=0\"$ .
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Look at $\"4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+5+%29-280=0\"$ .
Multiplied numerator integers
It becomes $\"4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_green%28+40+%29-280=0\"$ .
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Look at $\"4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+40+%29-highlight_red%28+280+%29=0\"$ .
Added fractions or integers together
It becomes $\"4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_green%28+-240+%29=0\"$ .
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Look at $\"4%2An%5E2%2B20%2An%2B8%2An%2Bhighlight_red%28+-240+%29=0\"$ .
Removed extra sign in front of $\"-240\"$
It becomes $\"4%2An%5E2%2B20%2An%2B8%2An-highlight_green%28+240+%29=0\"$ .
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Look at $\"4%2An%5E2%2Bhighlight_red%28+20%2An+%29%2Bhighlight_red%28+8%2An+%29-240=0\"$ .
Eliminated similar terms $\"highlight_red%28+20%2An+%29\"$ , $\"highlight_red%28+8%2An+%29\"$ replacing them with $\"highlight_green%28+%2820%2B8%29%2An+%29\"$
It becomes $\"4%2An%5E2%2Bhighlight_green%28+%2820%2B8%29%2An+%29-240=0\"$ .
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Look at $\"4%2An%5E2%2B%28highlight_red%28+20+%29%2Bhighlight_red%28+8+%29%29%2An-240=0\"$ .
Added fractions or integers together
It becomes $\"4%2An%5E2%2B%28highlight_green%28+28+%29%29%2An-240=0\"$ .
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Look at $\"4%2An%5E2%2Bhighlight_red%28+%28highlight_red%28+28+%29%29%2An+%29-240=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+28+%29\"$
It becomes $\"4%2An%5E2%2Bhighlight_green%28+28+%29%2An-240=0\"$ .
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Look at $\"highlight_red%28+4%2An%5E2%2B28%2An-240+%29=0\"$ .
Equation $\"highlight_red%28+4%2An%5E2%2B28%2An-240=0+%29\"$ is a quadratic equation: 4*n^2+28*n-240 =0, and has solutions 5,-12
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=5,n=-12.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Solution n=-12 will not work since lengths can only be positive. So the answer is 5. \n" ); document.write( "

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