Question

Use factoring and the zero-product property to solve:

Answer 1

\[2x^2+6x=0\]

Answer 2

\[\large\rm 2x\color{orangered}{x}+6\color{orangered}{x}=0\]What does each term have in common?
Hmm well they certainly have x in common,
I guess we can factor that out of each term,\[\large\rm \color{orangered}{x}(2x+6)=0\]What else do they have in common?
Both 2 and 6 are even numbers,
so they should be divisible by 2, right?

Answer 3

Yep, and sorry for taking long to reply~

Answer 4

So ya, pull a 2 out of each term,\[\large\rm 2x(x+3)=0\]the 6 loses a factor of 2, leaving a 3.
The 2x loses a 2, leaving an x.

Answer 5

Then apply your Zero-Factor Property:
\(\large\rm 2x=0\)
\(\large\rm (x+3)=0\)
Setting each individual factor equal to zero.
And solve for x in each equation.

Answer 6

Ah I see, I think I get it now.