Question

How do you factor `4x^2+7x=2`?

Answer 1

`(4x-1)(x+2)=0`

Explanation:

We can subtract `2` from both sides of this equation to set it equal to zero. We get

`4x^2+7x-2=0`

Now, we can factor by grouping. Here, we will split up the `b` term into two separate terms so we can factor more easily. We can rewrite this business as

`color(blue)(4x^2+8x)color(red)(-x-2)=0`

Notice, I rewrote `7x` as being equal to `8x-x`, so I didn't change the value of the expression.

We can factor out a `4x` out of the blue terms, and a `-1` out of the red terms. We get

`4x(x+2)-1(x+2)=0`

Both terms have an `(x+2)` in common, so we can factor that out to get

`(4x-1)(x+2)=0`

as our complete, factored answer.

Hope this helps!