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

May 23, 2018

$\left(4 x - 1\right) \left(x + 2\right) = 0$

#### Explanation:

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

$4 {x}^{2} + 7 x - 2 = 0$

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

$\textcolor{b l u e}{4 {x}^{2} + 8 x} \textcolor{red}{- x - 2} = 0$

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

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

$4 x \left(x + 2\right) - 1 \left(x + 2\right) = 0$

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

$\left(4 x - 1\right) \left(x + 2\right) = 0$