help with factoring please

Question

megan7 · Answer

$$x ^{2} + 4x=0$$

sammixboo · Answer

To help, I will do the first step for you.

$\tt x^2 + 4x = 0 \color{red}{\rightarrow} x(x+4) = 0$ 

Do you know why I did that?

megan7 · Answer

no that is what I am confused with

sammixboo · Answer

Change $\tt x^2+4x$ to $\tt x(x+4)$

megan7 · Answer

but how do I know to change it to that?

sammixboo · Answer

OK, let's look at the two terms $\tt x^2$ and $\tt4x$. Do you see a greatest common factor in the two terms?

megan7 · Answer

I don't think

megan7 · Answer

4?

sammixboo · Answer

Not quite. Do you know what a greatest common factor, or a factor, is?

megan7 · Answer

yes, I just don't know how to find it in that one

sammixboo · Answer

Well, your common factor would be $\tt x$, because x goes into $\tt x^2$ and $\tt 4x$. 

Think of $\tt x^2$ as $\tt x \times x$. Let's re-write our expression: $\tt x \times x + 4x$. What is a common factor between each term? It's x

megan7 · Answer

Ohh Okayy I see! Thank you so much!