document.write( "Question 38527This question is from textbook
\n" ); document.write( ": (3y+2)(y+3)=y+14 \n" ); document.write( "

Algebra.Com's Answer #24021 by Alwayscheerful(414) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: y=0.666666666666667,y=-4.
Graphical form: Equation $\"%283y%2B2%29%2A%28y%2B3%29=y%2B14\"$ was fully solved.
Text form: (3y+2)*(y+3)=y+14 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+%283y%2B2%29%2A%28y%2B3%29=y%2B14+%29\"$
For tutors: simplify_cartoon( (3y+2)*(y+3)=y+14 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"%283%2Ay%2B2%29%2A%28y%2B3%29=highlight_red%28+y%2B14+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-y+%29\"$ , $\"highlight_green%28+-14+%29\"$
It becomes $\"%283%2Ay%2B2%29%2A%28y%2B3%29-highlight_green%28+y+%29-highlight_green%28+14+%29=0\"$ .
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Look at $\"highlight_red%28+%283%2Ay%2B2%29%2A%28y%2B3%29+%29-y-14=0\"$ .
Expanded term $\"%28y%2B3%29\"$ by using associative property on $\"%283%2Ay%2B2%29\"$
It becomes $\"highlight_green%28+%28y%2B3%29%2A3%2Ay+%29%2Bhighlight_green%28+%28y%2B3%29%2A2+%29-y-14=0\"$ .
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Look at $\"highlight_red%28+%28y%2B3%29%2A3%2Ay+%29%2B%28y%2B3%29%2A2-y-14=0\"$ .
Expanded term $\"3%2Ay\"$ by using associative property on $\"%28y%2B3%29\"$
It becomes $\"highlight_green%28+3%2Ay%2Ay+%29%2Bhighlight_green%28+3%2Ay%2A3+%29%2B%28y%2B3%29%2A2-y-14=0\"$ .
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Look at $\"3%2Ay%2Ay%2Bhighlight_red%28+3+%29%2Ay%2Ahighlight_red%28+3+%29%2B%28y%2B3%29%2A2-y-14=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Ay%2Ay%2Bhighlight_green%28+9+%29%2Ay%2B%28y%2B3%29%2A2-y-14=0\"$ .
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Look at $\"3%2Ahighlight_red%28+y+%29%2Ahighlight_red%28+y+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+y+%29\"$ to $\"highlight_green%28+y%5E2+%29\"$
It becomes $\"3%2Ahighlight_green%28+y%5E2+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0\"$ .
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Look at $\"3%2Ay%5E2%2Bhighlight_red%28+9%2Ay+%29%2B%28y%2B3%29%2A2-highlight_red%28+y+%29-14=0\"$ .
Eliminated similar terms $\"highlight_red%28+9%2Ay+%29\"$ , $\"highlight_red%28+-y+%29\"$ replacing them with $\"highlight_green%28+%289-1%29%2Ay+%29\"$
It becomes $\"3%2Ay%5E2%2Bhighlight_green%28+%289-1%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0\"$ .
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Look at $\"3%2Ay%5E2%2B%28highlight_red%28+9+%29-highlight_red%28+1+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ay%5E2%2B%28highlight_green%28+8+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0\"$ .
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Look at $\"3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+8+%29%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+8+%29\"$
It becomes $\"3%2Ay%5E2%2Bhighlight_green%28+8+%29%2Ay%2B%28y%2B3%29%2A2-14=0\"$ .
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Look at $\"3%2Ay%5E2%2B8%2Ay%2Bhighlight_red%28+%28y%2B3%29%2A2+%29-14=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%28y%2B3%29\"$
It becomes $\"3%2Ay%5E2%2B8%2Ay%2Bhighlight_green%28+2%2Ay+%29%2Bhighlight_green%28+2%2A3+%29-14=0\"$ .
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Look at $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+3+%29-14=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+6+%29-14=0\"$ .
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Look at $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+6+%29-highlight_red%28+14+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+-8+%29=0\"$ .
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Look at $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+-8+%29=0\"$ .
Removed extra sign in front of $\"-8\"$
It becomes $\"3%2Ay%5E2%2B8%2Ay%2B2%2Ay-highlight_green%28+8+%29=0\"$ .
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Look at $\"3%2Ay%5E2%2Bhighlight_red%28+8%2Ay+%29%2Bhighlight_red%28+2%2Ay+%29-8=0\"$ .
Eliminated similar terms $\"highlight_red%28+8%2Ay+%29\"$ , $\"highlight_red%28+2%2Ay+%29\"$ replacing them with $\"highlight_green%28+%288%2B2%29%2Ay+%29\"$
It becomes $\"3%2Ay%5E2%2Bhighlight_green%28+%288%2B2%29%2Ay+%29-8=0\"$ .
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Look at $\"3%2Ay%5E2%2B%28highlight_red%28+8+%29%2Bhighlight_red%28+2+%29%29%2Ay-8=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ay%5E2%2B%28highlight_green%28+10+%29%29%2Ay-8=0\"$ .
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Look at $\"3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+10+%29%29%2Ay+%29-8=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+10+%29\"$
It becomes $\"3%2Ay%5E2%2Bhighlight_green%28+10+%29%2Ay-8=0\"$ .
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Look at $\"highlight_red%28+3%2Ay%5E2%2B10%2Ay-8+%29=0\"$ .
Equation $\"highlight_red%28+3%2Ay%5E2%2B10%2Ay-8=0+%29\"$ is a quadratic equation: 3*y^2+10*y-8 =0, and has solutions 0.666666666666667,-4
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: y=0.666666666666667,y=-4.

Universal Simplifier and Solver

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Done!

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