Example

Solve for $w$ by factoring: $\quad 4w^2+7w=-3$

Solution

We start by using algebra to get a zero on the right and everything else on the left:

Now we factor the left-hand side. I'll use the slide-and-divide method. See this sheet for reference.

In order to factor, we must find two numbers whose product is $(4)(3)=12$ and whose sum is $7$. Those numbers are $3$ and $4$. Therefore, the factorization of the left-hand side is given by

Now we solve the equation by setting the factors equal to zero.