document.write( "Question 36929: hi, i need help on these kind of problems solve for x, then write the equation as a polynomial. the problem is (x-3)(x-2)=0 thank you
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Algebra.Com's Answer #22685 by Alwayscheerful(414) $\"\"$ $\"About$

You can put this solution on YOUR website!
From just looking at the equation, there are going to be 2 values for x.
\n" ); document.write( "As long as one of the quantities equals zero, you multiply the other and you also get zero; therefore, you know the answer.
\n" ); document.write( "X = 3 or 2\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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Graphical form: $\"%28x-3%29%2A%28x-2%29\"$ simplifies to $\"x%5E2-5%2Ax%2B6\"$
Text form: (x-3)*(x-2) simplifies to x^2-5*x+6
Cartoon (animation) form: $\"simplify_cartoon%28+%28x-3%29%2A%28x-2%29+%29\"$
For tutors: simplify_cartoon( (x-3)*(x-2) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+%28x-3%29%2A%28x-2%29+%29\"$ .
Expanded term $\"%28x-2%29\"$ by using associative property on $\"%28x-3%29\"$
It becomes $\"highlight_green%28+%28x-2%29%2Ax+%29-highlight_green%28+%28x-2%29%2A3+%29\"$ .
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Look at $\"highlight_red%28+%28x-2%29%2Ax+%29-%28x-2%29%2A3\"$ .
Expanded term $\"x\"$ by using associative property on $\"%28x-2%29\"$
It becomes $\"highlight_green%28+x%2Ax+%29-highlight_green%28+x%2A2+%29-%28x-2%29%2A3\"$ .
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Look at $\"highlight_red%28+x+%29%2Ahighlight_red%28+x+%29-x%2A2-%28x-2%29%2A3\"$ .
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"highlight_green%28+x%5E2+%29-x%2A2-%28x-2%29%2A3\"$ .
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Look at $\"x%5E2-x%2A2-highlight_red%28+%28x-2%29%2A3+%29\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28x-2%29\"$
It becomes $\"x%5E2-x%2A2-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A2+%29\"$ .
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Look at $\"x%5E2-x%2A2-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29\"$ .
Multiplied numerator integers
It becomes $\"x%5E2-x%2A2-3%2Ax%2Bhighlight_green%28+6+%29\"$ .
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Look at $\"x%5E2-highlight_red%28+x%2A2+%29-highlight_red%28+3%2Ax+%29%2B6\"$ .
Eliminated similar terms $\"highlight_red%28+-x%2A2+%29\"$ , $\"highlight_red%28+-3%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-2-3%29%2Ax+%29\"$
It becomes $\"x%5E2%2Bhighlight_green%28+%28-2-3%29%2Ax+%29%2B6\"$ .
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Look at $\"x%5E2%2B%28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ax%2B6\"$ .
Added fractions or integers together
It becomes $\"x%5E2%2B%28highlight_green%28+-5+%29%29%2Ax%2B6\"$ .
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Look at $\"x%5E2%2B%28highlight_red%28+-5+%29%29%2Ax%2B6\"$ .
Removed extra sign in front of $\"-5\"$
It becomes $\"x%5E2%2B%28-highlight_green%28+5+%29%29%2Ax%2B6\"$ .
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Look at $\"x%5E2%2Bhighlight_red%28+%28-highlight_red%28+5+%29%29%2Ax+%29%2B6\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+5+%29\"$
It becomes $\"x%5E2-highlight_green%28+5+%29%2Ax%2B6\"$ .
Result: $\"x%5E2-5%2Ax%2B6\"$
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Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "Now you have your polynomial.
\n" ); document.write( " $\"x%5E2-5x%2B6=0\"$ \r
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