# Algebraic Expressions Simplified

#### loraboiago

##### New member
How does 3x or (x-5) equal 0 in the statement 3x(x-5)=0? I don't understand the logic behind it. Thank you!!

#### MarkFL

Staff member
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.

#### loraboiago

##### New member
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.
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?

#### MarkFL

Staff member
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?
I 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.

#### loraboiago

##### New member
I 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.
Ah got it! You are awesome. Thank you 