For quadratic equations, you need to factor in order to solve for your variable.  You do this after the equation is set equal to zero.  Thus, you get:

Next do your factoring.  You know that both groups will be negative.  This will give you a positive last factor but a negative middle term.  Given the value of the middle term, the factors of  needed will be  and 

Then, you set each factor equal to .  Solve each "small" equation:

 or 

 or 

BOTH of these are answers to the equation.

This is a quadratic equation, so first, move all terms to the same side by subtracting :

The quadratic polynomial can be factored using the  (or grouping) method. We want to split the middle term by finding two integers with sum  and product ; through some trial and error, we find  and . The equation becomes

Regroup:

Distribute out common factors as follows:

Since the product of these two binomial expressions is equal to 0, one of them is equal to 0; set both to 0 and solve:

Subtract 1 from both sides:

Divide both sides by 3:

or

Add 3 to both sides:

The solution set of the equation is .

Start by rearranging the given equation:

Next, factor the equation.

Finally, set each factor equal to zero and solve.

and

Since  can equal to either , we know that  must then equal to either .

Start by factoring the equation.

For this equation, you want two numbers that multiply up to  and add to . The only numbers that fit this criterion are  and .

Thus,

Now, set each of these factors equal to zero and solve.

Start by factoring the equation.

We will need two numbers that multiply up to  and add up to . These two numbers are .

Thus, we can factor the equation.

Solving the equation will give the following solutions:

and

Since the question states that  must be a positive integer,  can only equal to .

In order to solve this equation, you need to factor the expression, 

.

To do so, you need to find two factors of  that have a sum of  .

The two factors are  and  and the correct factoring is 

,

so you know that 

.

Therefore,  will be equal to any values that give the inside of the parentheses a value of .

So,  is equal to both  and .

Start by factoring the equation:

For this equation, we will want two numbers that add up to  and multiply up to . In this case, the two numbers are  and .

We can then write the following:

Now, set each factor equal to zero and solve for .

and

Start by factoring . Since one factor is already given to you, you just need to figure out what number when multiplied by  will give  and when added to  will give . The only number that fits both criteria is .  must be equal to .

We must start by factoring 

We must think of two numbers that multiply to be 15 and add to be 8. We come up with 3 and 5

Then

So we have

Which means either    or  

So,  or

Looking at , we notice that it is a perfect square trinomial.

*A perfect square trinomial is given by the form  (where "a" represents a variable term and "b" represents a constant term).

*Comparing this to our trinomial, we find...

*So, we confirm it is, indeed, a perfect square trinomial.

We have one solution: