document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917751>Question 917751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone explain why 8y(y-2)=0  = (y=0,y=2) I tried the problem solver, but I don't get it. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556787 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if a * b = 0 then either a = 0 or b = 0 or both = 0.<BR>\n" );
document.write( "have to be, otherwise the result will not be 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take that concept and apply it to 8y * (y-2) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let a = 8y<BR>\n" );
document.write( "let b = (y-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a * b = 0 becomes 8y * (y-2) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then either 8y = 0 or (y-2) = 0, otherwise the result will not be 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve each for 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8y = 0 results in y = 0 when you solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y-2 = 0 results in y = 2 when you solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm your results by substituting in the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "original equation is 8y * (y-2) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = 0, this becomes 0 * -2 = 0 which becomes 0 = 0 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = 2, this becomes 16 * 0 = 0 which becomes 0 = 0 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the original equation holds true when y = 0 or when y = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that confirms the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solver handled this no problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i entered 8y(y-2)=0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i also entered 8y*(y-2)=0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it handled both easily and said the solution was y = 0 or 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the explanations it gave under \"detailed\" may not be the best.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in fact, i had trouble understanding exactly what they were talking about.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if that's what you meant as to why you didn't get it, then i agree.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the reason is as i stated above.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if a * b = 0 then either a has to be equal to 0 or b has to be equal to 0 in order for the result to be equal to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both factors can also be equal to 0 at the same time, but that only occurs in special circumstances when the factors are either the same or mu;ltiples of each other.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(y-2) * (y-2) = 0<BR>\n" );
document.write( "both factors are equal to 0 when y = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "example again:<BR>\n" );
document.write( "(y-2) * (2y-4) = 0<BR>\n" );
document.write( "both factors are equal to 0 when y = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "having both factors equal to 0 at the same time is not essnetial.  only one of the factors has to be 0 in order for the result to be equal to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );