# How do you factor #6x^2 + 7x - 20 = 0#?

##### 3 Answers

A quadratic equation is simply another way of solving a problem if the solution cannot be factored logically.

First we can start with some quick review:

Let’s say we have the equation

To begin, we can state the factors of the first term,

Now we can check and see if any of the factors can combine in order to get a

From our factors we can use a -1 and a 3 to get +2. Therefore,

**However** , when the logical factorization seen above is not possible, we can plug our numbers into the *quadratic equation* .

After our a, b, and c values are found we can plug them into the actual quadratic equation.

*Note* : This equation may look intimidating, but as long as you follow factoring rules, you should have no problem. It’s totally normal to come out with an answer containing square roots.

Here's a somewhat mechanical approach:

To factor

You have

Multiply

Find two numbers whose product is

and whose sum is

Because we want the product to be negative, one number is positive and the other is negative.

Because we want the sum to be positive, the positive factor is the one with the greater absolute value.

We start the list:

**STOP** **the sum is**

Write

(Or by

Now factor by grouping:

Check the answer by multiplying.

The **"factoring box"** is a way of doing the factoring by grouping.

To use this box, you must first take out any factor that is common to all 3 terms. (If we had started with

Put the first and last terms in main diagonal (upper left and lower right) Then put in the two terms we found above

Notice that each row has common factors and each column has common factors (in some problems the only common factor is

and

We'll write those factors on a new first row and a new left column:

(The

The factors are the top row and the left column:

We can factorize it easily.

#### Explanation:

We need to multiply the coefficient of

The we put "(15-8)" before the the variable