document.write( "Question 1096723: What are all the real values of x which satisfy the equation: $\"+%28x-7%29%28x%5E2-6x%2B4%29=-%28x-7%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #711165 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

The first response missed one solution because he divided both sides of the equation by x-7. That turned out to be invalid, because x=7 is one of the solutions.

\n" ); document.write( "Never divide both sides of an equation by an expression containing a variable. Use factoring instead.

\n" ); document.write( "And the second solution gave the answers without showing the process....

\n" ); document.write( "So let me fill in the details, in case you are still not quite sure.

\n" ); document.write( " $\"%28x-7%29%28x%5E2-6x%2B4%29=-%28x-7%29\"$
\n" ); document.write( " $\"%28x-7%29%28x%5E2-6x%2B4%29+%2B+%28x-7%29+=+0\"$ [except for linear polynomials, you always want to get everything on one side set equal to 0 and then factor]
\n" ); document.write( " $\"%28x-7%29%28x%5E2-6x%2B5%29+=+0\"$
\n" ); document.write( " $\"%28x-7%29%28x-5%29%28x-1%29+=+0\"$

\n" ); document.write( "The solutions are x = 1, 5, and 7. \n" ); document.write( "

\n" );