Algebra-1

To solve the equation by factoring, let's rearrange it to bring all the terms to one side:

3x² + 5x - 12 = 0

Next, we're looking for two numbers whose product is equal to the product of the coefficient of x² (which is 3) and the constant term (which is -12). In other words, we have:

mn = ac

In this case, a = 3 and c = -12, so we have:

mn = 3 * (-12)
mn = -36

We're also looking for two numbers, m and n, such that their sum is equal to the coefficient of x (which is 5). In other words, we have:

m + n = b

In this case, b = 5.

Now let's find the values of m and n that satisfy these conditions. We need two numbers whose product is -36 and whose sum ...