# Solving a Quadratic Equation using Factoring

#### ILUvSKITTLEs44

##### New member
I don't understand my math homework. It wants me to solve a QUADRATIC EQUATION using factoring, but I don't really understand how to do this.

So its up to you people to help me try to figure out how to solve a "QUADRATIC EQUATION WHILE USING FACTORING"
Maggy

#### jwpaine

##### Full Member
Please show original problem. How are we supposed to help if we don't know what you're working on?

Thanks,
John.

#### Random

##### New member
A quadratic formula is simply a y=ax^2 + bx + c equation...
Lets say the problem asks you to factor:

$$\displaystyle y = x^2 + 5x - 6$$

The firsth term is $$\displaystyle x^2$$, so the first term in the facors will be x, because $$\displaystyle x*x= x^2$$.

The middle term is positive, and the last term is negative. Since the second terms in the factors must multiply together to equal the third term, and they must also add up to the second term, we know that the signs must be a + and a -.
We now have for the factors:
$$\displaystyle (x + ?)(x - ?)$$

What two numbers add up to 5 [from the middle term] and multiply together to equal -6? {6, -1}! So we plug these into the factors and we have:
$$\displaystyle (x+6)(x-1)$$
The completely factored formula looks like:

$$\displaystyle y = (x + 6)(x - 1)$$

Now to solve!

When you solve an equation, you set the y to 0, so
$$\displaystyle 0 = (x + 6)(x - 1)$$

Since you have the factors multiplying by eachother, you can split them apart and set them both to equal like:
$$\displaystyle 0 = (x + 6) and 0 = (x - 1)$$
Solve for x!
so the solution to the equation would be x={-6,1}!

#### Denis

##### Senior Member
ILUvSKITTLEs44 said:
So its up to you people to help me try to figure out how to solve a "QUADRATIC EQUATION WHILE USING FACTORING"
NO, it's up to your math teacher.

#### stapel

##### Super Moderator
Staff member
ILUvSKITTLEs44 said:
So its up to you people to help me try to figure out how to solve a "QUADRATIC EQUATION WHILE USING FACTORING"
So your class didn't cover simple factoring, special factoring, factoring quadratics, the Zero Factor Property, or solving quadratics...? How very frustrating for you! You might want to considering registering a complaint with the administration.

Unfortunately, we cannot provide the many hours of missing classroom instruction. Please consider hiring a tutor and/or doing some self-study. You can use your textbook, other help books (such as "Dummies" types of books at your library and/or book retailer), as well as online resources, such as:

. . . . .Google results for "simple factoring"

. . . . .Google results for "factoring quadratics"

. . . . .Google results for "special factoring"

. . . . .Google results for "zero product factor solve"

. . . . .Google results for "solving quadratics"

Once you have studied the relevant background material, please attempt whatever exercise you are working on. If you get stuck, please reply showing how far you have gotten.

Thank you! Eliz.