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#### loraboiago

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- Nov 29, 2013

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Thank you Mark for the quick and helpful response. The answer to this question went on to explain "3x(x-5)=0 provides an equation in which at least one of the expressions 3x or (x-5) is equal to 0. That translates into two possible values for x: 0 and 5."If you have the statement:

\(\displaystyle a\cdot b=0\) where \(\displaystyle a\ne b\)

Then the only way it can be true is if either \(\displaystyle a=0\) or \(\displaystyle b=0\). This is called the zero-factor property.

I understand how one can equal 0 (thanks to you!), but how do I calculate the other possible value as being 5?

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I would look at it as 3 factors being equal to zero:Thank you Mark for the quick and helpful response. The answer to this question went on to explain "3x(x-5)=0 provides an equation in which at least one of the expressions 3x or (x-5) is equal to 0. That translates into two possible values for x: 0 and 5."

I understand how one can equal 0 (thanks to you!), but how do I calculate the other possible value as being 5?

\(\displaystyle 3\cdot x\cdot(x-5)=0\)

Now, set all factors involving $x$ equal to zero, and then solve for $x$ in each equation:

\(\displaystyle x=0\)

\(\displaystyle x-5=0\)

The solutions to these equations will give you the solutions to the original equation.

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Ah got it! You are awesome. Thank youI would look at it as 3 factors being equal to zero:

\(\displaystyle 3\cdot x\cdot(x-5)=0\)

Now, set all factors involving $x$ equal to zero, and then solve for $x$ in each equation:

\(\displaystyle x=0\)

\(\displaystyle x-5=0\)

The solutions to these equations will give you the solutions to the original equation.