document.write( "Question 283328: 4x(x-9)-5x(x-8)=-5 \n" ); document.write( "

Algebra.Com's Answer #205698 by Deina(147) $\"\"$ $\"About$

You can put this solution on YOUR website!
First we need to simplify the equation:
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: x=-1,x=5.
Graphical form: Equation $\"4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=-5\"$ was fully solved.
Text form: 4*x*(x-9)-5*x*(x-8)=-5 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=-5+%29\"$
For tutors: simplify_cartoon( 4*x*(x-9)-5*x*(x-8)=-5 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29=highlight_red%28+-5+%29\"$ .
Moved these terms to the left $\"highlight_green%28+5+%29\"$
It becomes $\"4%2Ax%2A%28x-9%29-5%2Ax%2A%28x-8%29%2Bhighlight_green%28+5+%29=0\"$ .
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Look at $\"highlight_red%28+4%2Ax%2A%28x-9%29+%29-5%2Ax%2A%28x-8%29%2B5=0\"$ .
Expanded term $\"4%2Ax\"$ by using associative property on $\"%28x-9%29\"$
It becomes $\"highlight_green%28+4%2Ax%2Ax+%29-highlight_green%28+4%2Ax%2A9+%29-5%2Ax%2A%28x-8%29%2B5=0\"$ .
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Look at $\"4%2Ax%2Ax-highlight_red%28+4+%29%2Ax%2Ahighlight_red%28+9+%29-5%2Ax%2A%28x-8%29%2B5=0\"$ .
Multiplied numerator integers
It becomes $\"4%2Ax%2Ax-highlight_green%28+36+%29%2Ax-5%2Ax%2A%28x-8%29%2B5=0\"$ .
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Look at $\"4%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-36%2Ax-5%2Ax%2A%28x-8%29%2B5=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"4%2Ahighlight_green%28+x%5E2+%29-36%2Ax-5%2Ax%2A%28x-8%29%2B5=0\"$ .
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Look at $\"4%2Ax%5E2-36%2Ax-highlight_red%28+5%2Ax%2A%28x-8%29+%29%2B5=0\"$ .
Expanded term $\"-5%2Ax\"$ by using associative property on $\"%28x-8%29\"$
It becomes $\"4%2Ax%5E2-36%2Ax-highlight_green%28+5%2Ax%2Ax+%29%2Bhighlight_green%28+5%2Ax%2A8+%29%2B5=0\"$ .
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Look at $\"4%2Ax%5E2-36%2Ax-5%2Ax%2Ax%2Bhighlight_red%28+5+%29%2Ax%2Ahighlight_red%28+8+%29%2B5=0\"$ .
Multiplied numerator integers
It becomes $\"4%2Ax%5E2-36%2Ax-5%2Ax%2Ax%2Bhighlight_green%28+40+%29%2Ax%2B5=0\"$ .
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Look at $\"4%2Ax%5E2-36%2Ax-5%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29%2B40%2Ax%2B5=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"4%2Ax%5E2-36%2Ax-5%2Ahighlight_green%28+x%5E2+%29%2B40%2Ax%2B5=0\"$ .
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Look at $\"highlight_red%28+4%2Ax%5E2+%29-36%2Ax-highlight_red%28+5%2Ax%5E2+%29%2B40%2Ax%2B5=0\"$ .
Eliminated similar terms $\"highlight_red%28+4%2Ax%5E2+%29\"$ , $\"highlight_red%28+-5%2Ax%5E2+%29\"$ replacing them with $\"highlight_green%28+%284-5%29%2Ax%5E2+%29\"$
It becomes $\"highlight_green%28+%284-5%29%2Ax%5E2+%29-36%2Ax%2B40%2Ax%2B5=0\"$ .
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Look at $\"%284-5%29%2Ax%5E2-highlight_red%28+36%2Ax+%29%2Bhighlight_red%28+40%2Ax+%29%2B5=0\"$ .
Eliminated similar terms $\"highlight_red%28+-36%2Ax+%29\"$ , $\"highlight_red%28+40%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-36%2B40%29%2Ax+%29\"$
It becomes $\"%284-5%29%2Ax%5E2%2Bhighlight_green%28+%28-36%2B40%29%2Ax+%29%2B5=0\"$ .
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Look at $\"%28highlight_red%28+4+%29-highlight_red%28+5+%29%29%2Ax%5E2%2B%28-36%2B40%29%2Ax%2B5=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-1+%29%29%2Ax%5E2%2B%28-36%2B40%29%2Ax%2B5=0\"$ .
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Look at $\"%28-1%29%2Ax%5E2%2B%28-highlight_red%28+36+%29%2Bhighlight_red%28+40+%29%29%2Ax%2B5=0\"$ .
Added fractions or integers together
It becomes $\"%28-1%29%2Ax%5E2%2B%28highlight_green%28+4+%29%29%2Ax%2B5=0\"$ .
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Look at $\"%28highlight_red%28+-1+%29%29%2Ax%5E2%2B%284%29%2Ax%2B5=0\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"%28-highlight_green%28+1+%29%29%2Ax%5E2%2B%284%29%2Ax%2B5=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax%5E2+%29%2B%284%29%2Ax%2B5=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$
It becomes $\"-highlight_green%28+1+%29%2Ax%5E2%2B%284%29%2Ax%2B5=0\"$ .
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Look at $\"-1%2Ax%5E2%2Bhighlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29%2B5=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+4+%29\"$
It becomes $\"-1%2Ax%5E2%2Bhighlight_green%28+4+%29%2Ax%2B5=0\"$ .
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Look at $\"-highlight_red%28+1+%29%2Ax%5E2%2B4%2Ax%2B5=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"-x%5E2%2B4%2Ax%2B5=0\"$ .
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Look at $\"highlight_red%28+-x%5E2%2B4%2Ax%2B5+%29=0\"$ .
Equation $\"highlight_red%28+-x%5E2%2B4%2Ax%2B5=0+%29\"$ is a quadratic equation: -x^2+4*x+5 =0, and has solutions -1,5
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=-1,x=5.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Notice that this turns it into the quadratic $\"-x%5E2+%2B+4%2Ax+%2B+5+=+0\"$ , which you can solve as any standard quadratic in the form of $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ and bob's your uncle! \n" ); document.write( "

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