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 February 26th, 2012, 07:49 AM #1 Newbie   Joined: Feb 2012 Posts: 9 Thanks: 0 Solve a problem please!!! Quiz Monday (27x + 297)(15x -(-105))=0 I know it equals 0 But I have to show the work. There are two variables. CONFUSED???
 February 26th, 2012, 09:01 AM #2 Newbie   Joined: Feb 2012 From: Russia Posts: 12 Thanks: 0 Re: Solve a problem please!!! Quiz Monday $(27x+297)(15x-(-105))=0$ You have the product of two factors: $(27x+297)$ $(15x-(-105))$ It's clear that if the product of two factors is 0, at least one of the factors must be 0. So we have: The first factor: $27x+297=0,$ $27x=-297,$ $x=-297/27,$ $x=-11.$ The second factor: $15x-(-105)=0,$ $15x=-105,$ $x=-105/15,$ $x=-7.$ Answer: x = -11 OR x = -7. This equation has 2 roots.
 February 26th, 2012, 02:26 PM #3 Newbie   Joined: Feb 2012 Posts: 9 Thanks: 0 Re: Solve a problem please!!! Quiz Monday If the equation is simplified to equal x = -11 or x = -7 How does one of these equal 0
 February 26th, 2012, 04:18 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,205 Thanks: 512 Math Focus: Calculus/ODEs Re: Solve a problem please!!! Quiz Monday We are given: $(27x+297)(15x+105)=0$ Factor further: $27(x+11)\cdot15(x+7)=0$ Divide through by 27·15: $(x+11)(x+7)=0$ Now, by the zero-product property, if two factors are equal to zero, then the equation is true if either of the factors is equal to zero. So, what you do is take each factor in turn, equate to zero and solve for x: i) $x+11=0$ $x=-11$ ii) $x+7=0$ $x=-7$ These are the two values for x which are solutions to the original equation.

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